Introduction: noninteracting atomic gases; BoseEinstein distribution; condensation transition at low temperatures; cooling and trapping of atomic gases. Quantum scattering of two atoms: scattering length; description of atomatom interactions via pseudopotential.
GrossPitaevskii equation for the condensate wave function: dynamics of the condensate; free expansion; solitons. Microscopic description of a Bose gas: Bogoliubov transformation; elementary excitations; rotating condensates; synthetic magnetic fields for cold atoms; interference and correlations in condensates.
Optical lattices: dimensionality of lattices; energy scales; bands. BoseHubbard model. Superfluid to Mottinsulator transition. Cold atoms in low dimensional systems: BerezinskiiKosterlitzThouless ( BKT) transition in twodimensions, correlation functions and limit of strong interactions in onedimensional gases.
Introduction to Monte Carlo methods, pseudorandom numbers, random walk, error assessment. Variational Monte Carlo. Trial wave functions suitable for simulations of atoms, molecules, clusters, fluids and solids and their optimisation. Diffusion Monte Carlo. Fermions and excited states  sign problem. Determining expectation values of observables. Finitetemperature calculations: path integral quantum Monte Carlo. All methods will be accompanied by examples in the field of atomic and molecular physics and condensed matter physics

 Pethick, C. J., and H. Smith, 2008, BoseEinstein Condensation in Dilute Gases (Cambridge University Press, Cambridge, UK)
 Pitaevskii, L., and S. Stringari, 2003, BoseEinstein Condensation (Oxford University Press, UK)
 CohenTannoudji, C., and D. GueryOdelin, 2011, Advances In Atomic Physics: An Overview (World Scientific Publishing Company, Singapore)
 Lewenstein, M., A. Sanpera, and V. Ahufinger, 2012, Ultracold Atoms in Optical Lattices (Oxford University Press, Oxford, UK).
