As circunstâncias e motivações ligadas à criação do Curso Experimental de Ciências Moleculares em 1991 na Universidade de São Paulo são reconstruídas com base em testemunhos publicados de seus criadores e consideradas com relação aos sucessos e dificuldades havidas ao longo do amadurecimento do curso.

The circumstances and motivations leading to the creation in 1991 of the “Curso Experimental de Ciências Moleculares” (Molecular Science Experimental Course) at the University of São Paulo are reconstructed on the base of published testimonies of its creators. They are then considered in view of the successes and difficulties which were met along the maturing of the course.

Properties of the ground-state, zero temperature 'phase diagram' of the Bose-Hubbard hamiltonian as understood by Fisher et al. [5] are studied using simple tools in the case of nite systems. The results obtained provide a transparent picture of the thermodynamic limit and reveal features reminiscent of shell structure in many-fermion systems. Independent sites and many-site correlations appear in correspondence with independent fermions and many-fermion correlations respectively. This paper is dedicated to Nicim Zagury, on the occasion of his seventieth birthday.

The material presented here consists of lecture notes written for a five two-hour sections course given during the 2004 edition of the Brazilian School on Statistical Mechanics. The topics covered are 1. Bose-Einstein condensation of trapped ideal gases; 2. Effective two-body interactions and exact results in the Gross-Pitaevski limit; 3. Atomic structure effects, including "Feshbach resonances" and hybrid condensates; 4. Elementary excitations in the Bogoliubov approximation and beyond; and 5. Splitt traps, interference phenomena and condensate arrays.