The dynamics of atomic nuclei is amongst the most challenging problem to treat theoretically. The richness of phenomena occurring in heavy-ion collisions can only be studied within microscopic approaches where each nucleon is treated quantum mechanically. Our goal is to present recent advances on microscopic descriptions of low energy heavy-ion collisions. We present both formal aspects and practical applications of the time-dependent Hartree-Fock (TDHF) theory, giving a mean-?eld dynamics of the system. As an example, we study the fusion of nuclei and some competing processes. The TDHF theory has some intrinsic limitations: absence of tunneling below the Coulomb barrier, missing dissipative e?ects and quantum ?uctuations. Mean-?eld theories should be improved to properly account for these e?ects. Several approaches are presented which account for pairing and/or direct nucleon-nucleon collisions. Finally, we discuss recent progresses in exact ab-initio methods based on the stochastic mean-?eld concept. This book is addressed to master and PhD students and/or researchers who want a general overview on microscopic approaches applied to nuclear dynamics.

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