This two-volume book was written for students of technical colleges who have had the usual mathematical training. It contains just enough in­ formation to continue with a wide variety of engineering disciplines. It covers analytic geometry and linear algebra, differential and integral cal­ culus for functions of one and more variables, vector analysis, numerical and functional series (including Fourier series), ordinary differential equa­ tions, functions of a complex variable, Laplace and Fourier transforms, and equations of mathematical physics. This list itself demonstrates that the book covers the material for both a basic course in higher mathematics and several specialist sections that are important for applied problems. Hence, it may be used by a wide range of readers. Besides students in techni­ cal colleges and those starting a mathematics course, it may be found useful by engineers and scientists who wish to refresh their knowledge of some aspects of mathematics.We tried to give the fundamental material concisely and without dis­ tracting detail. We concentrated on the presentation of the basic ideas of linear algebra and analysis to make it detailed and as comprehensible as possible. Mastery of these ideas is a requirement to understand the later  material.The many examples also serve this aim. The examples were written to help students with the mechanics of solving typical problems.More than 600 diagrams are simple illustrations, clear enough to demonstrate the ideas and statements convincingly, and can be fairly easily reproduced.We were conscious not to burden the course with scrupulous proofs for theorems which have little practical application. As a rule we chose the proof (marked in the text with special symbols) that was constructive in nature or explained fundamental ideas that had been introduced, show­ ing how they work. This approach made it possible to devise algorithms for solving whole classes of important problems.In addition to the examples, we have included several carefully selected problems and exercises (around 1000) which should be of interest to those pursuing an independent mathematics course. The problems have the form of moderately sized theorems. They are very simple but are good training for those learning the fundamental ideas.