  We report a detailed theoretical study of the electronic structure, spectral
properties, and lattice parameters of bulk FeSe under pressure using a fully
charge self-consistent implementation of the density functional theory plus
dynamical mean-field theory method (DFT+DMFT). In particular, we perform a
structural optimization and compute the evolution of the lattice parameters
(volume, $c/a$ ratio, and the internal $z$ position of Se) and the electronic
structure of the tetragonal (space group $P4/nmm$) paramagnetic FeSe. Our
results for the lattice parameters are in good quantitative agreement with
experiment. The $c/a$ ratio is slightly overestimated by about $3$~\%,
presumably due to the absence of the van der Waals interactions between the
FeSe layers in our calculations. The lattice parameters determined within DFT
are off the experimental values by a remarkable $\sim$$6$-$15$~\%, implying a
crucial importance of electron correlations. Upon compression to $10$~GPa, the
$c/a$ ratio and the lattice volume show a decrease by $2$ and $10$~\%,
respectively, while the Se $z$ coordinate weakly increases by $\sim$$2$~\%.
Most importantly, our results reveal a topological change of the Fermi surface
(Lifshitz transition) which is accompanied by a two- to three-dimensional
crossover. Our results indicate a small reduction of the quasiparticle mass
renormalization $m^*/m$ by about $5$~\% for the $e$ and less than $1$~\% for
the $t_2$ states, as compared to ambient pressure. The behavior of the
momentum-resolved magnetic susceptibility $\chi({\bf q})$ shows no topological
changes of magnetic correlations under pressure, but demonstrates a reduction
of the degree of the in-plane $(\pi,\pi)$ stripe-type nesting. Our results for
the electronic structure and lattice parameters of FeSe are in good qualitative
agreement with recent experiments on its isoelectronic counterpart
FeSe$_{1-x}$S$_x$.
