  This Dissertation presents results of a thorough study of ultracold bosonic
and fermionic gases in three-dimensional and quasi-one-dimensional systems.
Although the analyses are carried out within various theoretical frameworks
(Gross-Pitaevskii, Bethe ansatz, local density approximation, etc.) the main
tool of the study is the Quantum Monte Carlo method in different modifications
(variational Monte Carlo, diffusion Monte Carlo, fixed-node Monte Carlo
methods). We benchmark our Monte Carlo calculations by recovering known
analytical results (perturbative theories in dilute limits, exactly solvable
models, etc.) and extend calculations to regimes, where the results are so far
unknown. In particular we calculate the equation of state and correlation
functions for gases in various geometries and with various interatomic
interactions.
