This textbook contains 26 lectures organized into five topics: i) Complex Analysis, ii) Variational Calculus, iii) Ordinary Differential Equations, iv) Integral Transformations, and v) Partial Differential Equations. For each topic, basic fundamental theorems and mathematical techniques are pintroduced and applied to solving  problems. This resource is intended as concise and well-structured, making it suitable for a one-semester course. It is aimed at second- or third-year undergraduate students with background in mathematics and physical science.