The concept of the quantum gas is introduced and illustrated by numerous examples. The fundamentals of the theory of collective phenomena in quantum Maxwellian gases are surveyed in a simple and readily assimilated form, and possible experimental studies are outlined. Particular attention is devoted to weakly-damped spin waves. The spectrum of these waves is calculated and the magnetic susceptibility generalized. The results obtained are compared with experimental data on spin waves in gaseous H$\uparrow$, $^3$He$\uparrow$, and $^3$He$\uparrow$--$^4$He quantum solutions. It is shown that, at low temperatures, spin-polarized Boltzmann gases exhibit longrange spin correlations which fall off as r$^{-1}$ at large distances. The equations of spin dynamics are solved for arbitrary temperatures and degrees of polarization, both in the weakly damped and diffusion regimes. The thermodynamics of spin-polarized gases and some of the features of transport phenomena are examined. Paramagnetic resonance and other collective effects in binary quantum gases are discussed. Magnetic and structural thermodynamic phase transitions in binary Maxwellian gases are predicted. Collective phenomena in semimagnetic semiconductors and analogous effects in the spectroscopy of Rydberg atoms and levitating electrons are discussed.