This compendium is designed as a review of basic mathematics topics and is mainly aimed at students who are looking for valuable help to integrate their knowledge and correct their deficiencies in the subject, as well as to succeed in the math admission test of the University of Florence. The topics covered are divided into five macro areas: Numbers, Powers and Radicals, Literal calculation, Equations, Inequalities and absolute value, Exponential and logarithmic functions. For each one of the topics, the fundamental theoretical notions are offered with specific examples and a selection of single questions, thanks to which the student can immediately check their knowledge. Moreover, there is also a section collecting all the answers to the questions with extensive examination on the correct process and on the possible errors. This analysis represents the real strength of this work since it allows students to self-evaluate and learn from their mistakes.