Here, you will find books that allow you to dig deeper and gain a more thorough understanding of Einstein's theories - using simple formulae and basic high school mathematics.
Born, Max: Einstein's theory of relativity
Dover Publications 1962
A classic introduction to special (and a bit of general) relativity, using only basic high school mathematics. In this way, readers who have seen a square root before and dimly remember what triangles were all about (calculus not required) can gain a much better understanding of Einstein's theories than from a mere prose description. However, given its age, the book does not include any modern developments of the theories and their applications.
Schutz, Bernard: Gravity from the Ground Up: An Introductory Guide to Gravity and General Relativity
Cambridge: Cambridge University Press 2004
A thorough and extensive presentation of pretty much all aspects of gravitational physics, from Newton to gravitational waves. Again, basic math skills are required, but nothing as fancy as quadratic equations or, god forbid, calculus. Schutz, one of the directors of the Albert-Einstein-Institute in Potsdam, uses many instructive examples to guide the reader through the world of gravity - from the basics to interplanetary space travel, from stellar equilibrium to galaxies, and of course Einstein's ideas are explored in depth: The basics of general relativity are patiently explained, and the last quarter of the book is devoted to relativistic astrophysics, from black holes and gravitational waves to cosmology. As a bonus, the book has its own web-site with helpful simulations, animations, exercises (with solutions). Heartily recommended for high school students as well as undergraduates.
Mermin, N. David: It's About Time
Princeton and Oxford: Princeton University Press 2005
Take a physicist bent on really understanding what relativity is all about, let him think long and hard about the subject and about the simplest way to teach it to non-physicists, add the ability to write exceptionally clear prose, and you have David Mermin's first book on special relativity, "Space and Time in Special Relativity". Let the author's ideas and views evolve and mature for about three decades, leavened by the experience of teaching special relativity to non-science students, pour the result into a highly readable form, and you get "It's About Time" - probably the best book for anyone who wants to understand the basics of special relativity using no more than the simplest geometry and algebra.
Giulini, Domenico: Special Relativity. A First Encounter
Oxford: Oxford University Press 2005
An excellent basic introduction to special relativity and its consequences. The first four chapters give an overview of the theory, from its history and its basic concepts and formulae to important applications in various areas of physics. In the fifth chapter, each section takes a closer look at some special aspect of relativistic physics, including the key experimental tests of the theory, the question of superluminal velocities, and more abstract concepts like the group property of Lorentz transformations. The text is very clear and concise. Great care is taken in including all those caveats that sometimes fall by the wayside in simplified texts about special relativity. All but a few parts of the presentation can be understood with the help of pre-calculus high school mathematics. While familiarity with vectors will be of advantage to the reader - vectors are briefly introduced and sometimes used in the manner of a short-hand notation -, it is by no means a prerequisite. The book can be recommended both to students - high school and beyond - looking for a brief introduction to Einstein's famous theory, and to anyone looking for a compact refresher course.