This book consists of two parts.

The first part presents the material of Applied Mathematics that is usually taught to first-year students of Engineering and Science Schools in Greek Universities. Special emphasis has been placed on applications and exercises in order to clearly understand the way we apply theory to solve mathematical problems that we encounter in the science we study.

The second part develops the package of Symbolic Algebra Mathematica®, which allows us to work and try to solve mathematical problems using a computer. It is essentially a programming language that combines the user's ability to simultaneously use symbolic, numerical, and graphical methods to solve mathematical problems.

Writing a book that deals with Applied Mathematics, especially for first-year students, should overcome two very basic difficulties. The first concerns the presentation of mathematical concepts, which must be clear and complete, while the second concerns convincing first-year students that what they read is the key to opening doors that will lead them to solve the mathematical problems they will encounter in their science, either during their studies or later as professionals.

The combination of acquiring knowledge of both the mathematical concepts presented in the first part of the book and the package of Symbolic Algebra developed in the second part, I hope and wish to be the stimulus that the reader needs to get to know the magical world of Mathematics in a modern way.