This book brings together the main ideas of introductory algebra. They grew out of lectures given at the university to junior students of mathematics and is designed for a one or two- semester course in algebra and presumes some prior knowledge of mathematics at the pre-university level. The authors goal is to present the subject of algebra from its basic foundation of logic that leads to the study of the real and complex number systems and subsequently sequences and series in the real number system. Since the evolution of algebra from its beginning is closely linked with problems of finding solutions to polynomial equations, this subject is introduced and discussed in Chapter 6 of the book. The subsequent topics of linear equations and matrices in Chapter 7 and vectors in Chapter 8 are consequent to the discussion of polynomials in the earlier chapter.