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These lectures introduce techniques that are used in the description ofsystems of particles and fields at high temperature (or density). These methodshave a broad range of physical applications. We shall discuss two specificapplications: one related to hot and dense matter composed of quarks andgluons, with temperatures in the tera Kelvin range, the other related toBose-Einstein condensation in ultra-cold gases, with temperatures in the nanoKelvin range. As we shall see, in both systems, long wavelength collectivephenomena lead to similar features, in spite of the huge difference in ordersof magnitude of the respective energy scales.

Quantum Fields at Finite Temperature "from tera to nano Kelvin"