This textbook has been designed to meet the needs of B.Sc. First and Second Semester students of Mathematics as per Common Minimum Syllabus prescribed for Universities and Colleges under the recommended National Education Policy 2020 in Maharashtra. This comprehensive textbook is an essential resource for students and educators alike, offering a thorough exploration of key mathematical concepts across Algebra, Trigonometry, and Differential Calculus. The book is divided into two papers. In Paper I: Algebra and Trigonometry, you'll embark on a journey through foundational topics such as Set Theory, Relations and Matrices, progressing to advanced theories of Equations and De Moivre's Theorem. The book meticulously covers important algebraic concepts like the Euclidean Algorithm, Linear Congruences and the Cayley-Hamilton Theorem, providing clear explanations and numerous examples. Paper II: Differential Calculus delves into Functions of Single and Two Variables, addressing fundamental theorems like Rolle's Theorem, Mean Value Theorems and their applications. The section also covers Maxima and Minima, Taylor's Series, Lagrange's Method and tackles various Indeterminate Forms with precision. Designed for clarity and depth, this textbook is ideal for undergraduate students who wish to develop a strong foundation in these critical areas of mathematics. Whether you're a student or a professional, these books are designed to provide you with a thorough understanding and practical approaches to these crucial areas of mathematics.