Understanding the dynamics of photoexcited carriers in solids is vital to the development of optoelectronics. Here I will present our studies of electron dynamics in solids using the optical pump – extreme ultraviolet (XUV) probe method, where snapshots of the dynamics of valence electrons are taken with the core-level absorption of sub-femtosecond long XUV pulses. In this talk, I will discuss our studies on the thermalization of electrons in nickel and dynamics of core-excitons in few-layer MoS₂. In the study of electron thermalization dynamics in nickel, I will discuss the measurement of electron temperature using core-level absorption spectroscopy and the build-up of thermalized electrons after photoexcitation. In the study of MoS₂, a two-dimensional material, I will show that the Mo N_2,3 edge absorption spectrum exhibits an approximately 3 eV red-shift as the material thickness is reduced from bulk to few-layer, suggesting the presence of strong excitonic effect and that quantum confinement and dielectric screening affect not only the optical properties of MoS₂ but also the core-level absorption. With XUV transient absorption spectroscopy, an order of magnitude increase of transition lifetime from sub-femtosecond to 3-5 fs during the reduction of material thickness is identified and the extent of the excitonic wavefunctions estimated to be approximately 2 Å, agreeing well with results of ab initio simulations on core-excitons of monolayer MoS₂.