Are mathematical concepts just creations of human mind, or are they a reflection of real world? Do mathematicians create mathematical concepts and theories or do they discover them? We do not know full answer to these questions, but many mathematicians are sympathetic to view that describes a certain reality, independent of humankind. In academic year 2006/2007, recently deceased Archbishop of Lublin, Rev. Prof. Jozef Życinski\footnote{Jozef Życinski (1948-2011) was a philosopher, theologian, an Archbishop of Lublin and grand chancellor of Catholic University of Lublin. He was author of more than 50 books and hundreds of papers on topics related to philosophy of science, philosophy of nature, cosmology and evolution. He was a member of Polish Academy of Science, Pontifical Council for Culture, European Academy of Science and Art in Salzburg and Russian Academy of Natural Sciences.} gave a series of lectures entitled Elements of Platonic in fundamentals of mathematics and book reviewed here is based on these lecture notes, edited by Rev. Prof. Michal Heller. The book begins by presenting two contrasting answers to questions posed above: {\it Empiricism states that is an expression of world constructed by human minds, $\dots$; Platonic states that describes a reality which predates any human activity $\dots$ \/}. The book gives various arguments in favour of both of these views, although author does not hide fact that he supports Plato's approach. In one of chapters author considers question regarding existence of mathematical objects and describes views of Brouwer, Hilbert, Popper and Ellis. Ellis proposed that {\it a given object should be viewed as being onitically real, if its presence leads to observable consequences in real world \/}. In turn, according to Brouwer, only those mathematical objects which can be effectively constructed should be viewed as real. Another chapter is devoted to controversies regarding fundamentals of mathematics. In this chapter author talks about Hilbert's work on proof of consistency of arithmetic as proposed by Gentzen, which was later overthrown by discoveries of G\{o}del, as well as Bourbaki's approach to fundamentals of mathematics. The next chapter considers concept of truth in mathematics, including comments on Tarski's theorem regarding undefinability of truth. Although book is of a philosophical nature, we find many examples from discipline of mathematics. As such, reader may learn about intuitionism of Brouwer, as well as the G\odel and L\owenheim-Skolem theorems and their philosophical aspects. The author also writes in an accessible style on many problems in pure mathematics, including Fermat's last theorem and Riemann hypothesis. While reading this book, I only found a few minor errors. For example, on page 63, instead of the roots of equation $\zeta(z)=0$, author should have written the roots of equation $\zeta(1/2+iz)=0$, since this is equation that Riemann had in mind in context of this reference.