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Redundancy analysis (RDA) is a canonical ordination technique combining regression and principal component analysis (PCA). RDA allows studying the relationship between a matrix of response data (i.e. the Y matrix) and a matrix of centred explanatory variables (i.e. the X matrix). RDA is a powerful tool to analyse the composition of community, especially since Legendre and Gallagher (2001) created transformed-RDA (transformation-based RDA called td-RDA).
In brief, RDA is a multivariate linear regression followed by a PCA of the matrix of fitted values. The RDA produces min[p, m, n-1] canonical axes, where n is the number of objects, p the number of response variables and m the number of degrees of freedom of the model.
Source: Borcard, D., Gillet, F., & Legendre, P. (2011). Numerical ecology with R (Vol. 2, p. 688). New York: Springer Legendre, P., & Gallagher, E. D. (2001). Ecologically meaningful transformations for ordination of species data. Oecologia, 129(2), 271-280