1 Introduction.- 2 The space of rough paths.- 3 Brownian motion as a rough path.- 4 Integration against rough paths.- 5 Stochastic integration and Itô's formula.- 6 Doob-Meyer type decomposition for rough paths.- 7 Operations on controlled rough paths.- 8 Solutions to rough differential equations.- 9 Stochastic differential equations.- 10 Gaussian rough paths.- 11 Cameron-Martin regularity and applications.- 12 Stochastic partial differential equations.- 13 Introduction to regularity structures.- 14 Operations on modelled distributions.- 15 Application to the KPZ equation.- References.- Index.

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