I want to study quasicrystals from mathematical point of view, but I'm having hard time finding materials about it. If you could suggest me some books, articles or papers, I would be glad.

The trouble with the quasicrystals is that the literature in this area is dominated by nonmathematical or pseudomathematical papers and books. In particular, just extracting a mathematical definition of a quasicrystal from this literature is not so easy. This situation is wellillustrated by the wikipedia article on quasicrystals and the MO discussion of this topic at What is the relation between Quasicrystals, Riemann Hypothesis, and PV numbers? The two papers that I found most enlightening and mathematical, address this problem headon (more on this below): [1]. A. Hof, "On diffraction by aperiodic structures", Commun. Math. Phys., 169 (1995), p. 2543. [2]. JB. Gouere, "Quasicrystals and almost periodicity", Commun. Math. Phys., 255 (2005), p. 655681. Both papers prove some nontrivial mathematical theorems, on the basis of these theorems one can then form two, somewhat different, mathematical definitions of a (quasi)crystal. Senchal's 2page long survey paper (see Mahmud's answer) or, better, her book (see Joseph's answer) is a good introduction, the trouble is that she does not prove anything in the book and that she could be sloppy with her definitions, for instance, she conflates functions, measures and distributions, which are needed for defining crystals. If you look in Senchal's book, you first get the following physical definitions of crystals: "A crystal is any solid with essentially discrete diffraction diagram." (This includes both traditional crystals and quasicrystals.) The word "essentially" will be the difference between different mathematical definitions, which one derives from [1] and [2]. A (mathematical) quasicrystal is a tiling $T$ of ${\mathbb R}^n$ by convex polytopes satisfying certain properties:
a. Here is Hof's definition of a crystal (Senchal's definition is taken from Hof's paper). Hof in [1] takes the autocorrelation function (actually, a distribution) $\gamma$ of $N$ and computes the (appropriately defined) Fourier transform $\hat\gamma$ of $\gamma$ (this is a mathematical interpretation of the "diffraction diagram"). Then $\hat\gamma$ is a measure $\mu$ which, in general, splits as a sum of two measures $\mu_d+\mu_c$: Discrete part $\mu_d$, which is supported on a certain countable subset of ${\mathbb R}^n$ and continuous part $\mu_c$. He proposes that "essentially discrete diffraction" means that $\mu_d$ is nonzero. Hof then proves that "standard" tilings indeed have nontrivial $\mu_d$ (According to [2], Hof even proves that $\mu_c=0$ in this case, but I did not check this). The trouble with this definition is that, as far as I can tell, there is no known purely geometric interpretation of the condition $\mu_d\ne 0$ in terms of the next $N$ itself (at least, none existed 6 years ago). b. Gouere [2] (his work is an extension of Hof's approach and of a work by Lagarias) works with a slightly different definition, i.e., that $\mu_c=0$ (such sets $N$ are called Patterson sets). His main result is a purely geometric interpretation (actually, several interpretations) of this condition, see Theorem 1.1 in [1]: Patterson sets are the sets which are almost periodic with respect to Besikovitch's metric. Remark 1. As far as I can tell from reading Freeman Dyson's paper here, definition of a quasicrystal that Dyson proposes is the one with $\mu_c=0$. Remark 2. Gouere does not propose that a Patterson set is the right definition of a crystal, this is just my take on his paper. Condition $\mu_c=0$ is more limited, but, in view of [2], is geometric and also covers "standard" examples, while the condition $\mu_d\ne 0$ is more general, but is nongeometric. 


If you are interested in the noncommutative geometry side of things, there is an overview article, The Noncommutative Geometry of Aperiodic Solids (pdf link) by Jean Bellissard. He writes the paper building up from the most basic possible physical concepts and makes the use of noncommutative geometry to study quasicrystals seem quite natural, and it is done in a mathematically rigorous manner. Edit: I should emphasize that this paper is about the physical side of quasicrystals, written from a mathematical perspective. I wasn't sure if that was what you wanted, as opposed to just the mathematical study of quasicrystals without regard for any related physics. 


You might want to consider reading the following excellent introduction to the subject: 


Quasicrystals and Geometry by Marjorie Senechal. A bit dated (1996) but still a place to start.
(Amazon link).



and finally a technical paper: 


Here is a hardtofind but worthy book from the point of view of statistical mechanics:
There has been some progress since the writing of the book, but the main question (the construction of a latticegas model with translationinvariant finite range interactions admitting a quasicrystalline phase) remains open. If you don't like statistical mechanics, there is enormous literature on aperiodic tilings. The book
has two chapters on aperiodic tilings. For a more uptodate account, I would recommend the lecture notes of Jarkko Kari. If you tell us more specifically, which aspect of it you would like to study, maybe we could help better. 


My favorite paper on this stuff is Applications of Group Cohomology to the Classification of Quasicrystal Symmetries (by Fisher and Rabson) If you want to study symmetries, then there is Howard Hiller's note Crystallography and Cohomology of Groups 

