Aims. We examined the velocity, density, and temperature structure of Taurus molecular cloud-1 (TMC-1), a filamentary cloud in a nearby quiescent star forming area, to understand its morphology and evolution. Methods. We observed high signal-to-noise (S/N), high velocity resolution NH 3 (1,1), and (2, 2) emission on an extended map. By fitting multiple hyperfine-split line profiles to the NH 3 (1, 1) spectra, we derived the velocity distribution of the line components and calculated gas parameters on several positions. Herschel SPIRE far-infrared continuum observations were reduced and used to calculate the physical parameters of the Planck Galactic Cold Clumps (PGCCs) in the region, including the two in TMC-1. The morphology of TMC-1 was investigated with several types of clustering methods in the parameter space consisting of position, velocity, and column density. Results. Our Herschel-based column density map shows a main ridge with two local maxima and a separated peak to the south-west. The H 2 column densities and dust colour temperatures are in the range of 0.5−3.3 × 10 22 cm −2 and 10.5−12 K, respectively. The NH 3 column densities and H 2 volume densities are in the range of 2.8−14.2 × 10 14 cm −2 and 0.4−2.8 × 10 4 cm −3 . Kinetic temperatures are typically very low with a minimum of 9 K at the maximum NH 3 and H 2 column density region. The kinetic temperature maximum was found at the protostar IRAS 04381+2540 with a value of 13.7 K. The kinetic temperatures vary similarly to the colour temperatures in spite of the fact that densities are lower than the critical density for coupling between the gas and dust phase. The k-means clustering method separated four sub-filaments in TMC-1 with masses of 32.5, 19.6, 28.9, and 45.9 M and low turbulent velocity dispersion in the range of 0.13−0.2 km s −1 . Conclusions. The main ridge of TMC-1 is composed of four sub-filaments that are close to gravitational equilibrium. We label these TMC-1F1 through F4. The sub-filaments TMC-1F1, TMC-1F2, and TMC-1F4 are very elongated, dense, and cold. TMC-1F3 is a little less elongated and somewhat warmer, and probably heated by the Class I protostar, IRAS 04381+2540, which is embedded in it. TMC-1F3 is approximately 0.1 pc behind TMC1-F1. Because of its structure, TMC-1 is a good target to test filament evolution scenarios.