In this thesis it is shown how some basic concepts and facts from linear algebra are applied to magic squares. Magic square, in the sense of a quadratic scheme filled with numbers in such a manner that the same value is obtained by adding up the entries in each row, each column and both diagonals, has a very long history as a popular object in recreational mathematics, but also as a topic of serious mathematical research. Observed as quadratic matrices over a field, usually the real number field, magic squares of order \(n\) constitute a vector space, with subspaces formed by squares of some particular types. The dimension of this space and some of its subspaces is determined. It is shown how a unique decomposition of a square with magic constant \({\mu}\) as the sum of one square with magic constant 0 and another one with all its elements equal to \(-\frac{\mu}{n}\) becomes useful to that purpose, as well as for exploration of the spectrum of a magic square. Some special types of magic squares are studied, as their structure leads to interesting results and constructions. Through the definitions, numerous examples and the proofs of propositions it is visible how suitable linear algebra is for research of magic squares. It is proven that every centrosymmetric magic square of even order is a singular matrix. On the other hand, for any given odd prime number n it is possible to build a classical, centrosymmetric magic square of order \(n\).