diff --git a/README.md b/README.md
index 5d851eb..4ee3c3d 100644
--- a/README.md
+++ b/README.md
@@ -1,2 +1,149 @@
-# HPML
-HPML is a high performance mathematics library for computational science & 3d applications
+# Mathematics Library for Computer Graphics & Numerical Computing
+
+- In-depth documention is embedded in the header files
+- You can find overview of the library in **Getting Started**  section
+
+#### Features
+
+- Vector Mathematics
+  
+  - 2D vectors
+  
+  - 3D Vectors
+  
+  - 4D Vectors
+
+- Matrix Mathematics
+  
+  - 2x2 Matrix operations
+  
+  - 3x3 Matrix operations [WIP]
+  
+  - 4x4 Matrix operations
+
+- Quaternion Mathematics
+  
+  - Interpolations
+  
+  - Rotations
+  
+  - Conversion to euler angles [WIP]
+  
+  - Euler angles to Quaternion [WIP]
+
+- Complex Mathematics [WIP]
+
+#### Getting Started
+
+###### Types
+
+| Mathematical Type | Description            | HPML Type   |
+| ----------------- | ---------------------- | ----------- |
+| Vector 2D         | a 2 dimensional vector | `vec2_t`    |
+| Vector 3D         | a 3 dimensional vector | `vec3_t`    |
+| Vector 4D         | a 4 dimensional vector | `vec4_t`    |
+| Quaternion        | a quaternion           | `quat_t`    |
+| Matrix 2x2        | a 2x2 square matrix    | `mat2_t`    |
+| Matrix 3x3        | a 3x3 square matrix    | `mat3_t `   |
+| Matrix 4x4        | a 4x4 square matrix    | `mat4_t`    |
+| Complex Number    | a complex number       | `complex_t` |
+
+#### Vectors
+
+2D Vectors
+
+```c
+vec2_t v = { 1.0f, 2.0f };              // initializer
+vec2_t position = vec2(1.3f, 4.5f);     // constructor function
+
+position = VEC2 { 4.5f, 3.2f };         // re-assigning th value
+
+// constant vectors
+vec2_t up = vec2_up(); // or vec2_down()
+vec2_t left = vec2_left(); // or vec2_right()
+
+vec2_t null_vector = vec2_null(); // or vec2_zero();
+
+if(vec2_is_null(null_vector))            // checks if the vector is null
+    printf("Vector is null\n");
+
+// adding & subtracting vectors
+vec2_t final_position = vec2_add(2, position, vec2_down());
+vec2_t another_position = vec2_sub(2, position, vec2_up());
+
+// adding & subtracting more than 2 vectors at once
+final_position = vec2_add(3, position, vec2_down(), vec2_left());
+another_position = vec2_sub(3, position, vec2_down(), vec2_left());
+
+// printing on the console window for debugging purpose
+vec2_print(final_position);        // final_position: (x, y)
+vec2_print(another_position);      // another_position: (x, y)
+
+// interpolations [linear interpolation, and spherical linear interpolation]
+vec2_t interpolated_vector = vec2_lerp(vec2(1.0f, 2.0f), vec2(4.0f, 5.0f), 0.2f);
+vec2_t slerped_vector = vec2_slerp(vec2(1.0f, 2.0f), vec2(4.0f, 5.0f), 0.2f);
+vec2_print(interpolated_vector);
+vec2_print(slerped_vector);
+
+```
+
+
+
+3D Vectors
+
+```c
+vec3_t v = { 1.0f, 2.0f, 3.0f };              // initializer
+vec3_t position = vec3(1.3f, 4.5f, 3.4f);     // constructor function
+
+position = VEC3 { 4.5f, 3.2f, 6.7f };         // re-assigning the value
+
+
+// constant vectors
+vec3_t up = vec3_up();     // or vec3_down()
+vec3_t left = vec3_left(); // or vec3_right()
+
+vec3_t null_vector = vec3_null(); // or vec3_zero()
+
+if(vec3_is_null(null_vector))
+    printf("Vector is null\n");         // checks if the vector is null
+
+
+// adding & subtracting vectors
+vec3_t final_position = vec3_add(2, position, vec3_down());
+vec3_t another_position = vec3_sub(2, position, vec2_up());
+
+// adding & subtracting more than 2 vectors at once
+final_position = vec3_add(3, position, vec3_down(), vec3_left());
+another_position = vec3_sub(3, position, vec3_down(), vec3_left());
+
+// printing on the console window for debugging purpose
+vec3_print(final_position);        // final_position: (x, y, z)
+vec3_print(another_position);      // another_position: (x, y, z)
+
+// interpolations [linear interpolation, and spherical linear interpolation]
+vec3_t interpolated_vector = vec3_lerp(vec2(1.0f, 2.0f, 5.0f), vec2(4.0f, 5.0f, 2.0f), 0.2f);
+vec3_t slerped_vector = vec3_slerp(vec2(1.0f, 2.0f, 5.0f), vec2(4.0f, 5.0f, 2.0f), 0.2f);
+vec3_print(interpolated_vector);
+vec3_print(slerped_vector);
+
+```
+
+
+
+
+
+#### Matrices [TODO]
+
+#### Quaternions [TODO]
+
+#### Complex Numbers [TODO]
+
+
+
+### About me
+
+[Youtube](https://www.youtube.com/channel/UCWe_os3p4z3DBnQ4B5DUTfw/videos)
+
+[LinkedIn](https://www.linkedin.com/in/ravi-prakash-095a271a8/)
+
+[GitHub](https://github.com/ravi688)
diff --git a/include/hpml/complex.h b/include/hpml/complex.h
new file mode 100644
index 0000000..3834adb
--- /dev/null
+++ b/include/hpml/complex.h
@@ -0,0 +1,19 @@
+
+
+#pragma once
+
+
+typedef union complex_t
+{
+	struct 
+	{
+		float x, y;			// catesian coordiantes
+	};
+
+	struct
+	{
+		float r, arg; 		// polar coordinates
+	};
+} complex_t;
+
+
diff --git a/source/complex.c b/source/complex.c
new file mode 100644
index 0000000..bdf821c
--- /dev/null
+++ b/source/complex.c
@@ -0,0 +1,3 @@
+
+#include <hpml/complex.h>
+