This course provides an introduction to modern theoretical neuroscience with an attempt to cover all relevant spatial scales (from molecules to brain areas) as well as temporal scales (sub-millisecond to evolutionary time scales). An emphasis is put on models describing the subcellular machinery of neurons (e.g. synapses, ion channels), single neurons, networks of neurons, cortical circuits, columnar systems and interacting brain regions. Both functional and developmental aspects are discussed. Applications include representations of sensory inputs by neural circuits, with an emphasis on the mammalian visual system, short-term memory, multi-model integration and decision making.