QUIJOTE Scientific results. III. Microwave spectrum of intensity and polarization in the Taurus molecular cloud Complex and L1527

We present new intensity and polarization observations of the Taurus molecular cloud (TMC) region in the frequency range 10-20 GHz with the Multi-Frequency Instrument (MFI) mounted on the first telescope of the QUIJOTE experiment. From the combination of the QUIJOTE data with the WMAP 9-yr data release, the Planck second data release, the DIRBE maps and ancillary data, we detect an anomalous microwave emission (AME) component with flux density $S_{\rm AME, peak} = 43.0 \pm 7.9\,$Jy in the Taurus Molecular Cloud (TMC) and $S_{\rm AME, peak} = 10.7 \pm 2.7\,$Jy in the dark cloud nebula L1527, which is part of the TMC. In the TMC the diffuse AME emission peaks around a frequency of 19 GHz, compared with an emission peak about a frequency of 25 GHz in L1527. In the TMC, the best constraint on the level of AME polarisation is obtained at the Planck channel of 28.4 GHz, with an upper limit $\pi_{\rm AME}