The three parts of this textbook are based on the lecture notes Algebra I -III published by the present authors in the Slovak langauge. This textbook presents those three volumes of lecture notes together as one unit of Basic Algebra. Parts I and II of this textbook are aimed at and can be used as the teaching material for the existing courses Algebra I: Algebraic structures and Algebra II: Polynomial algebra at UMB. Part III can be used for course Linear algebra I.