BNT162b2, a nucleoside-modified mRNA formulated in lipid nanoparticles that encodes the SARS-CoV-2 spike glycoprotein (S) stabilized in its prefusion conformation, has demonstrated 95% efficacy in preventing COVID-191. Here we extend a previous phase-I/II trial report2 by presenting data on the immune response induced by BNT162b2 prime-boost vaccination from an additional phase-I/II trial in healthy adults (18-55 years old). BNT162b2 elicited strong antibody responses: at one week after the boost, SARS-CoV-2 serum geometric mean 50% neutralizing titres were up to 3.3-fold above those observed in samples from individuals who had recovered from COVID-19. Sera elicited by BNT162b2 neutralized 22 pseudoviruses bearing the S of different SARS-CoV-2 variants. Most participants had a strong response of IFNγ+ or IL-2+ CD8+ and CD4+ T helper type 1 cells, which was detectable throughout the full observation period of nine weeks following the boost. Using peptide-MHC multimer technology, we identified several BNT162b2-induced epitopes that were presented by frequent MHC alleles and conserved in mutant strains. One week after the boost, epitope-specific CD8+ T cells of the early-differentiated effector-memory phenotype comprised 0.02-2.92% of total circulating CD8+ T cells and were detectable (0.01-0.28%) eight weeks later. In summary, BNT162b2 elicits an adaptive humoral and poly-specific cellular immune response against epitopes that are conserved in a broad range of variants, at well-tolerated doses.