Knowledge in Elementary Algebra (E.A.) is the watershed between succeeding and failing in mathematics. This book bridges the gap between secondary school and university, enhancing undergraduate students' ability to pass mathematical analysis courses. The content of the book treats E.A. in many aspects, exploring the topics of formulas, rewriting expressions (expansion, factorization, division into partial fractions etc), solving equations as well as inequalities, and logics in connection with equation solving. This material has been used to diagnose and improve the mathematical level of first-year engineering students for a decade.