"This Marie Curie Career Integration Grant proposal entitled ""Quantum Gases in Synthetic Gauge Fields"" addresses the behaviour of ultracold atoms under the presence of synthetic gauge fields. The experimental techniques of creating synthetic gauge fields through optical methods have been pioneered recently by groups in the EU and US. Such methods have been used to produce large effective magnetic fields in optical lattice systems (corresponding to 10^4 Tesla in solid state systems).In addition, more general gauge fields have been created including spin-orbit coupling, which paves the way to the realisation of bands with nontrivial topology. Atoms under synthetic gauge fields represent fundamentally new states of quantum matter. In this proposal, I discuss how I will solve several important and experimentally relevant problems in this field. In particular, I will address the low temperature ordering of bosons with Rashba spin-orbitcoupling, edge state instabilities of bosons in topological bands created through synthetic fields, the behaviour of bosons in a flat-band model (dice lattice), and the controlled quantum dynamics of sodium spinor condensates under synthetic fields. The proposedresearch brings together ideas from diverse fields including condensed matter physics, atomic and molecular physics, quantum optics, spintronics, quantum information, and topology."