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These lecture notes have been written for a short introductory course on thestatus of inflation after Planck and BICEP2, given at the Xth Modave School ofMathematical Physics. The first objective is to give an overview of the theoryof inflation: motivations, homogeneous scalar field dynamics, slow-rollapproximation, linear theory of cosmological perturbations, classification ofsingle field potentials and their observable predictions. This includes apedagogical derivation of the primordial scalar and tensor power spectra forany effective single field potential. The second goal is to present the mostrecent results of Planck and BICEP2 and to discuss their implications forinflation. Bayesian statistical methods are introduced as a tool for modelanalysis and comparison. Based on the recent work of J. Martin et al., the bestinflationary models after Planck and BICEP2 are presented. Finally a series ofopen questions and issues related to inflation are mentioned and brieflydiscussed.

An introduction to inflation after Planck: from theory to observations