Infertility is a growing problem in all developed countries. The standard methods for the diagnostic of male infertility examine the concentration, motility and morphological anomalies of individual sperm cells. However, one in five male infertility cases remain unexplained with the standard diagnostic tools. In this thesis, we will explore the possibility to determine the male infertility causes from the detailed analysis of 3D trajectories and morphology of sperms swimming freely in the environment mimicking the conditions in the female reproductive tract. For this challenging task, we will develop a dedicated microscope based on holography for fast imaging and tracking of individual sperm cells. Along with classical numerical methods, we will use up-to date artificial intelligence algorithms for improving the imaging quality as well as for analysis of multi-dimensional data. Throughout the project we will closely collaborate with medical research institute (CHU/IAB) specialized in Assisted Reproductive Technologies (ART). We will be examining real patient samples in order to develop a new tool for male infertility diagnosis.