  The Snowmass 2021 Accelerator Frontier topical group \# 6 on Advanced
Accelerator Concepts, covers new R\&D concepts for particle acceleration,
generation, and focusing. Based on community input, this report describes how
leveraging these concepts to efficiently harness the interaction of charged
particles with extremely high electromagnetic fields at very high frequencies
can provide the keys to reaching ultra high acceleration gradients (GeV/m and
beyond). These methods have potential to reduce the dimensions, C0$_2$
footprint, and costs of future high energy physics machines, with added
potential to reduce power consumption for future e+e- and $\gamma - \gamma$
machines to and beyond 15 TeV energies. Techniques range from laser and beam
driven plasma and advanced structure accelerators to advanced phase space
manipulations and generation of beams with extreme parameters.
