An all-sky redshift survey of galaxies detected by the IRAS satellite was used to investigate the topology of the Universe to a depth of 200 h -1 Mpc. Qualitatively, the distribution of galaxies out to this distance resembles a Gaussian density field with a sponge-like topology : high- and low-density regions are topologically similar and surfaces of constant density are interconnected. Quantitatively, the genus-theshold density relation of Gott et al. (1989, ApJ, 340) was used to test the hypothesis that the galaxy distribution grew out of initially Gaussian density fluctuations and to measure the effective slope of the power spectrum of fluctuations over a range of length-scales between 10 and 50 h -1 Mpc