diff --git a/Mathematics/contracts/mlib.clar b/Mathematics/contracts/mlib.clar
index fdbde04..5815bca 100644
--- a/Mathematics/contracts/mlib.clar
+++ b/Mathematics/contracts/mlib.clar
@@ -1,15 +1,312 @@
+;; Enhanced Math Library in Clarity
+;; A comprehensive mathematical utility library with robust error handling
+;; and a diverse set of common mathematical operations.
 
-;; mlib
-;; <add a description here>
+;; ========== Constants ==========
 
-;; constants
-;;
+(define-constant ERR-OVERFLOW u"Arithmetic overflow occurred")
+(define-constant ERR-UNDERFLOW u"Arithmetic underflow occurred")
+(define-constant ERR-DIVIDE-BY-ZERO u"Cannot divide by zero")
+(define-constant ERR-NEGATIVE-ROOT u"Cannot compute square root of negative number")
+(define-constant ERR-NEGATIVE-LOG u"Cannot compute logarithm of non-positive number")
+(define-constant ERR-DOMAIN-ERROR u"Input value outside valid domain")
 
-;; data maps and vars
-;;
+;; ========== Basic Arithmetic Functions ==========
 
-;; private functions
-;;
+;; Addition Function with overflow check
+;; @param a (int) - First integer operand
+;; @param b (int) - Second integer operand
+;; @returns (response int string) - Returns result or error message
+(define-read-only (add (a int) (b int))
+  (let ((result (+ a b)))
+    (if (or 
+          ;; Check if signs are the same and overflow occurred
+          (and (> a 0) (> b 0) (< result 0))
+          (and (< a 0) (< b 0) (> result 0)))
+        (err ERR-OVERFLOW)
+        (ok result))))
 
-;; public functions
-;;
+;; Subtraction Function with underflow check
+;; @param a (int) - First integer operand
+;; @param b (int) - Second integer operand
+;; @returns (response int string) - Returns result or error message
+(define-read-only (subtract (a int) (b int))
+  (let ((result (- a b)))
+    (if (or
+          ;; Check for underflow scenarios
+          (and (> a 0) (< b 0) (< result a))
+          (and (< a 0) (> b 0) (> result a)))
+        (err ERR-UNDERFLOW)
+        (ok result))))
+
+;; Multiplication Function with improved overflow check
+;; @param a (int) - First integer operand
+;; @param b (int) - Second integer operand
+;; @returns (response int string) - Returns result or error message
+(define-read-only (multiply (a int) (b int))
+  (let ((result (* a b)))
+    (if (or (is-eq a 0) (is-eq b 0))
+        (ok 0)
+        (if (or 
+              (is-eq (/ result a) b) 
+              (is-eq (/ result b) a))
+            (ok result)
+            (err ERR-OVERFLOW)))))
+
+;; Division Function with error handling
+;; @param a (int) - Numerator
+;; @param b (int) - Denominator
+;; @returns (response int string) - Returns result or error message
+(define-read-only (divide (a int) (b int))
+  (if (is-eq b 0)
+      (err ERR-DIVIDE-BY-ZERO)
+      (ok (/ a b))))
+
+;; Safe division that returns a specified value on division by zero
+;; @param a (int) - Numerator
+;; @param b (int) - Denominator
+;; @param default (int) - Default value to return if b is zero
+;; @returns (int) - Result of division or default value
+(define-read-only (safe-divide (a int) (b int) (default int))
+  (if (is-eq b 0)
+      default
+      (/ a b)))
+
+;; ========== Integer Math Functions ==========
+
+;; Square Function (a^2) with overflow protection
+;; @param a (int) - Input value
+;; @returns (response int string) - Returns squared value or error message
+(define-read-only (square (a int))
+  (multiply a a))
+
+;; Cube Function (a^3) with overflow protection
+;; @param a (int) - Input value
+;; @returns (response int string) - Returns cubed value or error message
+(define-read-only (cube (a int))
+  (match (multiply a a)
+    success (multiply success a)
+    error error))
+
+;; Power Function for integers with overflow protection
+;; Only works with non-negative exponents
+;; @param base (int) - Base value
+;; @param exponent (uint) - Exponent (must be non-negative)
+;; @returns (response int string) - Returns result or error message
+(define-read-only (power (base int) (exponent uint))
+  (if (is-eq exponent u0)
+      (ok 1)  ;; anything^0 = 1
+      (if (is-eq base 0)
+          (ok 0)  ;; 0^n = 0 for n > 0
+          (if (is-eq exponent u1)
+              (ok base)  ;; n^1 = n
+              (let ((half-exp (/ exponent u2))
+                    (odd (is-eq (mod exponent u2) u1)))
+                (match (power base half-exp)
+                  half-result (match (multiply half-result half-result)
+                                squared (if odd
+                                           (multiply squared base)
+                                           (ok squared))
+                                error error)
+                  error error))))))
+
+;; Integer square root approximation 
+;; Returns the largest integer r such that r*r <= n
+;; @param n (uint) - Input value
+;; @returns (response uint string) - Returns integer square root or error message
+(define-read-only (isqrt (n uint))
+  (if (is-eq n u0)
+      (ok u0)
+      (let ((x u1)
+            (y (+ (/ n u2) u1)))
+        (ok (isqrt-iter x y n)))))
+
+;; Helper function for isqrt using Newton's method
+(define-private (isqrt-iter (x uint) (y uint) (n uint))
+  (if (< x y)
+      (isqrt-iter y (/ (+ (/ n y) y) u2) n)
+      x))
+
+;; Modular Function (renamed to avoid conflict with built-in 'mod' function)
+;; @param a (int) - Dividend
+;; @param b (int) - Divisor
+;; @returns (response int string) - Returns remainder or error message
+(define-read-only (modular (a int) (b int))
+  (if (is-eq b 0)
+      (err ERR-DIVIDE-BY-ZERO)
+      (ok (mod a b))))
+
+;; Absolute Value Function
+;; @param a (int) - Input value
+;; @returns (response int string) - Returns absolute value or error message
+(define-read-only (absolute (a int))
+  (if (< a 0)
+      (let ((result (- 0 a)))
+        (if (< result 0)  ;; Check for MIN_INT case
+            (err ERR-OVERFLOW)
+            (ok result)))
+      (ok a)))
+
+;; Sign Function
+;; Returns -1 for negative numbers, 0 for zero, and 1 for positive numbers
+;; @param a (int) - Input value
+;; @returns (int) - Sign of the input value
+(define-read-only (sign (a int))
+  (if (> a 0)
+      1
+      (if (< a 0)
+          -1
+          0)))
+
+;; ========== Statistical Functions ==========
+
+;; Average Function with overflow protection
+;; @param a (int) - First value
+;; @param b (int) - Second value
+;; @returns (response int string) - Returns average value or error message
+(define-read-only (average (a int) (b int))
+  (match (add a b)
+    sum-result (divide sum-result 2)
+    error error))
+
+;; Calculate weighted average of two values
+;; @param a (int) - First value
+;; @param weight-a (uint) - Weight for first value
+;; @param b (int) - Second value
+;; @param weight-b (uint) - Weight for second value
+;; @returns (response int string) - Returns weighted average or error message
+(define-read-only (weighted-average (a int) (weight-a uint) (b int) (weight-b uint))
+  (if (and (is-eq weight-a u0) (is-eq weight-b u0))
+      (err ERR-DIVIDE-BY-ZERO)
+      (let ((total-weight (+ weight-a weight-b)))
+        (match (multiply a (to-int weight-a))
+          weighted-a (match (multiply b (to-int weight-b))
+                       weighted-b (match (add weighted-a weighted-b)
+                                    sum (divide sum (to-int total-weight))
+                                    error error)
+                       error error)
+          error error))))
+
+;; ========== Comparison Functions ==========
+
+;; Maximum Function
+;; @param a (int) - First value
+;; @param b (int) - Second value
+;; @returns (int) - Larger of the two values
+(define-read-only (maximum (a int) (b int))
+  (if (>= a b) a b))
+
+;; Minimum Function
+;; @param a (int) - First value
+;; @param b (int) - Second value
+;; @returns (int) - Smaller of the two values
+(define-read-only (minimum (a int) (b int))
+  (if (<= a b) a b))
+
+;; Clamp Function
+;; Restricts a value to a specified range
+;; @param value (int) - Value to clamp
+;; @param min-val (int) - Minimum bound
+;; @param max-val (int) - Maximum bound
+;; @returns (int) - Clamped value
+(define-read-only (clamp (value int) (min-val int) (max-val int))
+  (if (< value min-val)
+      min-val
+      (if (> value max-val)
+          max-val
+          value)))
+
+;; ========== Number Property Functions ==========
+
+;; Is Even Function
+;; @param a (int) - Input value
+;; @returns (bool) - True if the value is even, false otherwise
+(define-read-only (is-even (a int))
+  (is-eq (mod a 2) 0))
+
+;; Is Odd Function
+;; @param a (int) - Input value
+;; @returns (bool) - True if the value is odd, false otherwise
+(define-read-only (is-odd (a int))
+  (not (is-eq (mod a 2) 0)))
+
+;; Is Positive Function
+;; @param a (int) - Input value
+;; @returns (bool) - True if the value is positive, false otherwise
+(define-read-only (is-positive (a int))
+  (> a 0))
+
+;; Is Negative Function
+;; @param a (int) - Input value
+;; @returns (bool) - True if the value is negative, false otherwise
+(define-read-only (is-negative (a int))
+  (< a 0))
+
+;; Is Divisible By Function
+;; @param a (int) - Dividend
+;; @param b (int) - Divisor
+;; @returns (response bool string) - Returns divisibility check or error message
+(define-read-only (is-divisible-by (a int) (b int))
+  (if (is-eq b 0)
+      (err ERR-DIVIDE-BY-ZERO)
+      (ok (is-eq (mod a b) 0))))
+
+;; ========== Utility Conversion Functions ==========
+
+;; Convert int to uint if possible
+;; @param a (int) - Input integer
+;; @returns (response uint string) - Returns uint or error message
+(define-read-only (int-to-uint (a int))
+  (if (< a 0)
+      (err ERR-DOMAIN-ERROR)
+      (ok (to-uint a))))
+
+;; Convert uint to int safely
+;; @param a (uint) - Input unsigned integer
+;; @returns (response int string) - Returns int or error message
+(define-read-only (uint-to-int (a uint))
+  (let ((result (to-int a)))
+    (if (< result 0)  ;; Check for overflow
+        (err ERR-OVERFLOW)
+        (ok result))))
+
+;; ========== Bitwise Operations ==========
+
+;; Bitwise AND operation
+;; @param a (uint) - First operand
+;; @param b (uint) - Second operand
+;; @returns (uint) - Result of bitwise AND
+(define-read-only (bitwise-and (a uint) (b uint))
+  (bit-and a b))
+
+;; Bitwise OR operation
+;; @param a (uint) - First operand
+;; @param b (uint) - Second operand
+;; @returns (uint) - Result of bitwise OR
+(define-read-only (bitwise-or (a uint) (b uint))
+  (bit-or a b))
+
+;; Bitwise XOR operation
+;; @param a (uint) - First operand
+;; @param b (uint) - Second operand
+;; @returns (uint) - Result of bitwise XOR
+(define-read-only (bitwise-xor (a uint) (b uint))
+  (bit-xor a b))
+
+;; Left shift operation
+;; @param a (uint) - Value to shift
+;; @param b (uint) - Shift amount
+;; @returns (uint) - Result of left shift
+(define-read-only (left-shift (a uint) (b uint))
+  (if (> b u128)
+      u0  ;; Shift by more than the bit width results in 0
+      (bit-shift-left a b)))
+
+;; Right shift operation
+;; @param a (uint) - Value to shift
+;; @param b (uint) - Shift amount
+;; @returns (uint) - Result of right shift
+(define-read-only (right-shift (a uint) (b uint))
+  (if (> b u128)
+      u0  ;; Shift by more than the bit width results in 0
+      (bit-shift-right a b)))
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