diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/domains/DoubleDomain.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/domains/DoubleDomain.kt
index 057a4a344..154763159 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/domains/DoubleDomain.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/domains/DoubleDomain.kt
@@ -24,7 +24,6 @@ import space.kscience.kmath.misc.UnstableKMathAPI
  */
 @UnstableKMathAPI
 public interface DoubleDomain : Domain<Double> {
-
     /**
      * Global lower edge
      * @param num axis number
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/linear/LinearSolver.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/linear/LinearSolver.kt
index af136c552..3e2dbee3f 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/linear/LinearSolver.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/linear/LinearSolver.kt
@@ -3,7 +3,10 @@ package space.kscience.kmath.linear
 import space.kscience.kmath.nd.as1D
 
 /**
- * A group of methods to resolve equation A dot X = B, where A and B are matrices or vectors
+ * A group of methods to solve for *X* in equation *X = A <sup>-1</sup> &middot; B*, where *A* and *B* are matrices or
+ * vectors.
+ *
+ * @param T the type of items.
  */
 public interface LinearSolver<T : Any> {
     /**
@@ -23,7 +26,7 @@ public interface LinearSolver<T : Any> {
 }
 
 /**
- * Convert matrix to vector if it is possible
+ * Convert matrix to vector if it is possible.
  */
 public fun <T : Any> Matrix<T>.asVector(): Point<T> =
     if (this.colNum == 1)
@@ -31,4 +34,11 @@ public fun <T : Any> Matrix<T>.asVector(): Point<T> =
     else
         error("Can't convert matrix with more than one column to vector")
 
+/**
+ * Creates an n &times; 1 [VirtualMatrix], where n is the size of the given buffer.
+ *
+ * @param T the type of elements contained in the buffer.
+ * @receiver a buffer.
+ * @return the new matrix.
+ */
 public fun <T : Any> Point<T>.asMatrix(): VirtualMatrix<T> = VirtualMatrix(size, 1) { i, _ -> get(i) }
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/linear/LinearSpace.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/linear/LinearSpace.kt
index 6a587270b..921f4c79c 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/linear/LinearSpace.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/linear/LinearSpace.kt
@@ -17,6 +17,8 @@ public typealias Matrix<T> = Structure2D<T>
 
 /**
  * Alias or using [Buffer] as a point/vector in a many-dimensional space.
+ *
+ * @param T the type of elements contained in the buffer.
  */
 public typealias Point<T> = Buffer<T>
 
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/Algebra.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/Algebra.kt
index 9f57bc4c1..960b7581c 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/Algebra.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/Algebra.kt
@@ -100,8 +100,8 @@ public fun <T : Any> Algebra<T>.bindSymbol(symbol: Symbol): T = bindSymbol(symbo
 public inline operator fun <A : Algebra<*>, R> A.invoke(block: A.() -> R): R = run(block)
 
 /**
- * Represents linear space without neutral element, i.e. algebraic structure with associative, binary operation [add]
- * and scalar multiplication [multiply].
+ * Represents group without neutral element (also known as inverse semigroup), i.e. algebraic structure with
+ * associative, binary operation [add].
  *
  * @param T the type of element of this semispace.
  */
@@ -177,7 +177,7 @@ public interface GroupOperations<T> : Algebra<T> {
 }
 
 /**
- * Represents linear space with neutral element, i.e. algebraic structure with associative, binary operation [add].
+ * Represents group, i.e. algebraic structure with associative, binary operation [add].
  *
  * @param T the type of element of this semispace.
  */
@@ -189,8 +189,8 @@ public interface Group<T> : GroupOperations<T> {
 }
 
 /**
- * Represents rng, i.e. algebraic structure with associative, binary, commutative operation [add] and associative,
- * operation [multiply] distributive over [add].
+ * Represents ring without multiplicative and additive identities, i.e. algebraic structure with
+ * associative, binary, commutative operation [add] and associative, operation [multiply] distributive over [add].
  *
  * @param T the type of element of this semiring.
  */
@@ -238,7 +238,7 @@ public interface Ring<T> : Group<T>, RingOperations<T> {
 }
 
 /**
- * Represents field without identity elements, i.e. algebraic structure with associative, binary, commutative operations
+ * Represents field without without multiplicative and additive identities, i.e. algebraic structure with associative, binary, commutative operations
  * [add] and [multiply]; binary operation [divide] as multiplication of left operand by reciprocal of right one.
  *
  * @param T the type of element of this semifield.
@@ -276,10 +276,11 @@ public interface FieldOperations<T> : RingOperations<T> {
 }
 
 /**
- * Represents field, i.e. algebraic structure with three operations: associative "addition" and "multiplication",
- * and "division" and their neutral elements.
+ * Represents field, i.e. algebraic structure with three operations: associative, commutative addition and
+ * multiplication, and division. **This interface differs from the eponymous mathematical definition: fields in KMath
+ * also support associative multiplication by scalar.**
  *
- * @param T the type of element of this semifield.
+ * @param T the type of element of this field.
  */
 public interface Field<T> : Ring<T>, FieldOperations<T>, ScaleOperations<T>, NumericAlgebra<T> {
     override fun number(value: Number): T = scale(one, value.toDouble())
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BigInt.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BigInt.kt
index 55bb68850..b5e27575b 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BigInt.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BigInt.kt
@@ -12,8 +12,8 @@ import kotlin.math.max
 import kotlin.math.min
 import kotlin.math.sign
 
-public typealias Magnitude = UIntArray
-public typealias TBase = ULong
+private typealias Magnitude = UIntArray
+private typealias TBase = ULong
 
 /**
  * Kotlin Multiplatform implementation of Big Integer numbers (KBigInteger).
@@ -358,6 +358,9 @@ private fun stripLeadingZeros(mag: Magnitude): Magnitude {
     return mag.sliceArray(IntRange(0, resSize))
 }
 
+/**
+ * Returns the absolute value of the given value [x].
+ */
 public fun abs(x: BigInt): BigInt = x.abs()
 
 /**
diff --git a/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/Piecewise.kt b/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/Piecewise.kt
index d2470a4b4..3510973be 100644
--- a/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/Piecewise.kt
+++ b/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/Piecewise.kt
@@ -2,14 +2,28 @@ package space.kscience.kmath.functions
 
 import space.kscience.kmath.operations.Ring
 
+/**
+ * Represents piecewise-defined function.
+ *
+ * @param T the piece key type.
+ * @param R the sub-function type.
+ */
 public fun interface Piecewise<T, R> {
+    /**
+     * Returns the appropriate sub-function for given piece key.
+     */
     public fun findPiece(arg: T): R?
 }
 
+/**
+ * Represents piecewise-defined function where all the sub-functions are polynomials.
+ */
 public fun interface PiecewisePolynomial<T : Any> : Piecewise<T, Polynomial<T>>
 
 /**
- * Ordered list of pieces in piecewise function
+ * Basic [Piecewise] implementation where all the pieces are ordered by the [Comparable] type instances.
+ *
+ * @param T the comparable piece key type.
  */
 public class OrderedPiecewisePolynomial<T : Comparable<T>>(delimiter: T) :
     PiecewisePolynomial<T> {
@@ -17,8 +31,10 @@ public class OrderedPiecewisePolynomial<T : Comparable<T>>(delimiter: T) :
     private val pieces: MutableList<Polynomial<T>> = arrayListOf()
 
     /**
-     * Dynamically add a piece to the "right" side (beyond maximum argument value of previous piece)
-     * @param right new rightmost position. If is less then current rightmost position, a error is thrown.
+     * Dynamically adds a piece to the right side (beyond maximum argument value of previous piece)
+     *
+     * @param right new rightmost position. If is less then current rightmost position, an error is thrown.
+     * @param piece the sub-function.
      */
     public fun putRight(right: T, piece: Polynomial<T>) {
         require(right > delimiters.last()) { "New delimiter should be to the right of old one" }
@@ -26,13 +42,19 @@ public class OrderedPiecewisePolynomial<T : Comparable<T>>(delimiter: T) :
         pieces.add(piece)
     }
 
+    /**
+     * Dynamically adds a piece to the left side (beyond maximum argument value of previous piece)
+     *
+     * @param left the new leftmost position. If is less then current rightmost position, an error is thrown.
+     * @param piece the sub-function.
+     */
     public fun putLeft(left: T, piece: Polynomial<T>) {
         require(left < delimiters.first()) { "New delimiter should be to the left of old one" }
         delimiters.add(0, left)
         pieces.add(0, piece)
     }
 
-    override fun findPiece(arg: T): Polynomial<T>? {
+    public override fun findPiece(arg: T): Polynomial<T>? {
         if (arg < delimiters.first() || arg >= delimiters.last())
             return null
         else {
@@ -46,9 +68,10 @@ public class OrderedPiecewisePolynomial<T : Comparable<T>>(delimiter: T) :
 }
 
 /**
- * Return a value of polynomial function with given [ring] an given [arg] or null if argument is outside of piecewise definition.
+ * Return a value of polynomial function with given [ring] an given [arg] or null if argument is outside of piecewise
+ * definition.
  */
 public fun <T : Comparable<T>, C : Ring<T>> PiecewisePolynomial<T>.value(ring: C, arg: T): T? =
     findPiece(arg)?.value(ring, arg)
 
-public fun <T : Comparable<T>, C : Ring<T>> PiecewisePolynomial<T>.asFunction(ring: C): (T) -> T? = { value(ring, it) }
\ No newline at end of file
+public fun <T : Comparable<T>, C : Ring<T>> PiecewisePolynomial<T>.asFunction(ring: C): (T) -> T? = { value(ring, it) }
diff --git a/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/Polynomial.kt b/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/Polynomial.kt
index 049909fe1..550785812 100644
--- a/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/Polynomial.kt
+++ b/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/Polynomial.kt
@@ -10,16 +10,26 @@ import kotlin.math.max
 import kotlin.math.pow
 
 /**
- * Polynomial coefficients without fixation on specific context they are applied to
- * @param coefficients constant is the leftmost coefficient
+ * Polynomial coefficients model without fixation on specific context they are applied to.
+ *
+ * @param coefficients constant is the leftmost coefficient.
  */
 public inline class Polynomial<T : Any>(public val coefficients: List<T>)
 
+/**
+ * Returns a [Polynomial] instance with given [coefficients].
+ */
 @Suppress("FunctionName")
 public fun <T : Any> Polynomial(vararg coefficients: T): Polynomial<T> = Polynomial(coefficients.toList())
 
+/**
+ * Evaluates the value of the given double polynomial for given double argument.
+ */
 public fun Polynomial<Double>.value(): Double = coefficients.reduceIndexed { index, acc, d -> acc + d.pow(index) }
 
+/**
+ * Evaluates the value of the given polynomial for given argument.
+ */
 public fun <T : Any, C : Ring<T>> Polynomial<T>.value(ring: C, arg: T): T = ring {
     if (coefficients.isEmpty()) return@ring zero
     var res = coefficients.first()
@@ -35,19 +45,23 @@ public fun <T : Any, C : Ring<T>> Polynomial<T>.value(ring: C, arg: T): T = ring
 }
 
 /**
- * Represent the polynomial as a regular context-less function
+ * Represent the polynomial as a regular context-less function.
  */
 public fun <T : Any, C : Ring<T>> Polynomial<T>.asFunction(ring: C): (T) -> T = { value(ring, it) }
 
 /**
- * An algebra for polynomials
+ * Space of polynomials.
+ *
+ * @param T the type of operated polynomials.
+ * @param C the intersection of [Ring] of [T] and [ScaleOperations] of [T].
+ * @param ring the [C] instance.
  */
 public class PolynomialSpace<T : Any, C>(
     private val ring: C,
 ) : Group<Polynomial<T>>, ScaleOperations<Polynomial<T>> where C : Ring<T>, C : ScaleOperations<T> {
     public override val zero: Polynomial<T> = Polynomial(emptyList())
 
-    override fun Polynomial<T>.unaryMinus(): Polynomial<T> = with(ring) {
+    override fun Polynomial<T>.unaryMinus(): Polynomial<T> = ring {
         Polynomial(coefficients.map { -it })
     }
 
@@ -64,6 +78,9 @@ public class PolynomialSpace<T : Any, C>(
     public override fun scale(a: Polynomial<T>, value: Double): Polynomial<T> =
         ring { Polynomial(List(a.coefficients.size) { index -> a.coefficients[index] * value }) }
 
+    /**
+     * Evaluates the polynomial for the given value [arg].
+     */
     public operator fun Polynomial<T>.invoke(arg: T): T = value(ring, arg)
 }
 
diff --git a/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/integration/Integrator.kt b/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/integration/Integrator.kt
index ebc53ad2e..e421fb680 100644
--- a/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/integration/Integrator.kt
+++ b/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/integration/Integrator.kt
@@ -1,11 +1,11 @@
 package space.kscience.kmath.integration
 
 /**
- * A general interface for all integrators
+ * A general interface for all integrators.
  */
 public interface Integrator<I : Integrand> {
     /**
-     * Run one integration pass and return a new [Integrand] with a new set of features
+     * Runs one integration pass and return a new [Integrand] with a new set of features.
      */
     public fun integrate(integrand: I): I
-}
\ No newline at end of file
+}
diff --git a/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/integration/UnivariateIntegrand.kt b/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/integration/UnivariateIntegrand.kt
index 9389318e8..ca4bbf6b8 100644
--- a/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/integration/UnivariateIntegrand.kt
+++ b/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/integration/UnivariateIntegrand.kt
@@ -61,4 +61,4 @@ public fun UnivariateIntegrator<Double>.integrate(
     return integrate(
         UnivariateIntegrand(function, *features.toTypedArray())
     ).value ?: error("Unexpected: no value after integration.")
-}
\ No newline at end of file
+}
diff --git a/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/interpolation/SplineInterpolator.kt b/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/interpolation/SplineInterpolator.kt
index ddbe743f0..ef75a1ef8 100644
--- a/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/interpolation/SplineInterpolator.kt
+++ b/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/interpolation/SplineInterpolator.kt
@@ -8,8 +8,11 @@ import space.kscience.kmath.operations.invoke
 import space.kscience.kmath.structures.MutableBufferFactory
 
 /**
- * Generic spline interpolator. Not recommended for performance critical places, use platform-specific and type specific ones.
- * Based on https://github.com/apache/commons-math/blob/eb57d6d457002a0bb5336d789a3381a24599affe/src/main/java/org/apache/commons/math4/analysis/interpolation/SplineInterpolator.java
+ * Generic spline interpolator. Not recommended for performance critical places, use platform-specific and type
+ * specific ones.
+ *
+ * Based on
+ * https://github.com/apache/commons-math/blob/eb57d6d457002a0bb5336d789a3381a24599affe/src/main/java/org/apache/commons/math4/analysis/interpolation/SplineInterpolator.java
  */
 public class SplineInterpolator<T : Comparable<T>>(
     public override val algebra: Field<T>,
diff --git a/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/interpolation/XYPointSet.kt b/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/interpolation/XYPointSet.kt
index 1ff7b6351..2b1312c0f 100644
--- a/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/interpolation/XYPointSet.kt
+++ b/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/interpolation/XYPointSet.kt
@@ -3,13 +3,40 @@ package space.kscience.kmath.interpolation
 import space.kscience.kmath.nd.Structure2D
 import space.kscience.kmath.structures.Buffer
 
+/**
+ * Pair of associated buffers for X and Y axes values.
+ *
+ * @param X the type of X values.
+ * @param Y the type of Y values.
+ */
 public interface XYPointSet<X, Y> {
+    /**
+     * The size of all the involved buffers.
+     */
     public val size: Int
+
+    /**
+     * The buffer of X values.
+     */
     public val x: Buffer<X>
+
+    /**
+     * The buffer of Y values.
+     */
     public val y: Buffer<Y>
 }
 
+/**
+ * Triple of associated buffers for X, Y, and Z axes values.
+ *
+ * @param X the type of X values.
+ * @param Y the type of Y values.
+ * @param Z the type of Z values.
+ */
 public interface XYZPointSet<X, Y, Z> : XYPointSet<X, Y> {
+    /**
+     * The buffer of Z values.
+     */
     public val z: Buffer<Z>
 }