In fundamental interactions research, dipolar magnets are particularly interesting to study since they provide a large spectrum of quantum phenomena [1-2]. Magnetic dipolar interaction are omnipresent in magnetic systems. However, in most of materials, various exchange interactions within the crystal environment hide the purely dipolar interaction. It has been shown [2-3] that in LiRF4 family, where R is a rare earth element the exchange interactions with nearest neighbours can be neglected. Moreover, by simply changing the R ion in the tetrafluoride lithium matrix, the magnetic behaviour can completely differ at low temperature. For instance LiHoF4 is a Ising ferromagnet , while LiErF4 is a XY antiferromagnet  and LiTmF4 a Van Vleck paramagnet . In order to understand theses systems, a detailed comprehension of the electronic crystal field is necessary, since the ground state is determined by this interaction . The energy range corresponds typically to the infrared region. While a lot of studies have been done in other LiRF4, LiTmF4 has not be fully investigated. This work presents the spectroscopy analysis from the far to the near infrared regions (10−100000 cm −1) of a pure LiTmF4 single crystal at cryogenic temperatures using Fourier transform Spectroscopy technique. The first part details the structure and the energy scale. The experimental details and FTIR spectroscopy will be then presented. The third chapter is dedicated to explain how the energy levels have been assigned and their strength. The results for the first three manifolds are presented and exhibit some intriguing results such as splitting. Finally, one will discuss the perspectives.