Starting from our big universe to the microscopic world, phase transitions play an important role in nature. Just after the Big Bang our universe experienced multiple phase transitions, from high-temperature plasma to the matter we know today. Phase transitions involve many properties, including mechanical, thermal, optical, electric, and magnetic, which represent the bedrock of our scientific and technological advances. Understanding the phase transitions and revealing their mechanism is a key step to controlling them and manipulating the desired properties of matter. It has been demonstrated that the dimensionality of a system is a crucial parameter in the involvement of phase transformations. The 3D phase transformations are classified into two categories: discontinuous ones, called first-order, and continuous ones, called second-order. In contrast to 3D systems, 2D ones admit intermediate phases which are not present in purely 3D systems, for example, a mixed state between solid and liquid, which is known by the name of hexatic phase. In this thesis, two systems with different dimensionality, 2D and 3D, are studied. In the 2D system, the phase diagram of a prototypical 2D material, which is argon adsorbed on graphite, is investigated. This system exhibits a complex phase diagram of pressure vs. temperature which is explored at low temperatures and low pressures constructing a deposition kinetic diagram. The presence of a mixed configuration exhibiting characters common to hexatic and liquid crystal configurations is hypothesized. The melting process of this material is explored in two ways: quasi-adiabatic and out-of-equilibrium driven by ultrafast laser pulses. The ultrafast dynamics in a timescale of picoseconds revealed an expansion of the argon films as a reaction to the dynamics of the substrate (graphite) photoexcited at 1.55 eV. In the 3D case, the first-order transition in magnetite, which involves structural and electronic transitions, the so-called Verwey transition is investigated. Following the transition from cubic to monoclinic in the quasi-adiabatic regime (temperature dependence) allowed tracking the symmetry of the order parameter involved in this structural transition. Photoexciting magnetite with two different photoexcitations, 1.55 and 3.10 eV, in the monoclinic phase below Verwey temperature, revealed two different processes, each one involving metastable intermediate states that are thermodynamically inaccessible. The photoexcitation at 1.55 eV promoted a phase separation between cubic metallic islands and monoclinic insulating zones. The photoexcitation at 3.10 eV reinforced the monoclinic insulating state by optimizing the long-range network of the trimerons. These investigations are conducted by means of Ultrafast Electron Diffraction (UED), thanks to the capabilities of this technique of probing the structural properties of crystals based on diffraction phenomena, with femtosecond (1e-15 s) and atomic (1e-10 m) temporal and spatial resolution. The results in this thesis validate the capability of this technique of studying complex phenomena, such as phase transitions, in both regimes, thermodynamic equilibrium and out-of-equilibrium.