Mathematics is a vast and fascinating field that forms the foundation of many scientific and engineering disciplines. A sound knowledge of this subject will help diploma and degree students develop analytical skills and thus enable them to solve numerical problems encountered in real life. This book aims to provide a comprehensive understanding of four fundamental areas of mathematics: logarithms, trigonometry, vector analysis, and the geometry of points and lines. The crisp and complete explanation of topics will help students easily understand the basic concepts. Each of these topics plays a crucial role in various applications, from solving complex equations to modelling real-world phenomena.