Covariant quantization of the superstring

After reviewing the Green-Schwarz superstring using the approach of Siegel, the superstring is covariantly quantised by constructing a BRST operator f rom the fermionic constraints and a bosonic pure spinor ghost variable. Phy sical massless vertex operators are constructed and, for the first time, N- point tree amplitudes are computed in a manifestly ten-dimensional super-Po incare covariant manner. Quantization can be generalized to curved supergra vity backgrounds and the vertex operator for fluctuations around AdS(5) x S -5 is explicitly constructed.