  Major astrophysical questions related to the formation and evolution of
structures, and more specifically of galaxy groups and clusters, will still be
open in the coming decade and beyond: what is the interplay of galaxy,
supermassive black hole, and intergalactic gas evolution in the most massive
objects in the Universe - galaxy groups and clusters? What are the processes
driving the evolution of chemical enrichment of the hot diffuse gas in
large-scale structures? How and when did the first galaxy groups in the
Universe, massive enough to bind more than 10^7 K gas, form? Focussing on the
period when groups and clusters assembled (0.5<z<2.5), we show that, due to the
continuum and line emission of this hot intergalactic gas at X-ray wavelengths,
Athena+, combining high sensitivity with excellent spectral and spatial
resolution, will deliver breakthrough observations in view of the
aforementioned issues. Indeed, the physical and chemical properties of the hot
intra-cluster gas, and their evolution across time, are a key to understand the
co-evolution of galaxy and supermassive black hole within their environments.
