This textbook is aimed at first- and second-year undergraduate mathematics students at universities, primarily those studying actuarial and financial mathematics at the Faculty of Mathematics and Mechanics, Yerevan State University. Mathematical analysis is generally found by students to be one of their hardest courses in mathematics. The main goal of this book is to rigorously present the fundamental concepts of mathematical analysis in the clearest, simplest way, within the context of illuminating graphs, diagrams and examples. Topics covered include all the basic concepts and methods of mathematical analysis such as the limit of a sequence or a function, continuous and differentiable functions, the investigation of functions and the construction of their graphs, indefinite and Riemann definite integrals, improper integrals, numerical, functional and power series, functions of bounded variation, the Riemann-Stieltjes integral. It also covers multivariable calculus including local and constrained extrema, and the double integral. The textbook is suitable for self-study or for use in parallel with a standard university course on the subject.