LOFAR 150-MHz observations of the Boötes field: catalogue and source counts

We present the first wide area (19 deg$^2$), deep ($\approx120-150$ {\mu}Jy beam$^{-1}$), high resolution ($5.6 \times 7.4$ arcsec) LOFAR High Band Antenna image of the Bo\"otes field made at 130-169 MHz. This image is at least an order of magnitude deeper and 3-5 times higher in angular resolution than previously achieved for this field at low frequencies. The observations and data reduction, which includes full direction-dependent calibration, are described here. We present a radio source catalogue containing 6276 sources detected over an area of $19$\,deg$^2$, with a peak flux density threshold of $5\sigma$. As the first thorough test of the facet calibration strategy, introduced by van Weeren et al., we investigate the flux and positional accuracy of the catalogue. We present differential source counts that reach an order of magnitude deeper in flux density than previously achieved at these low frequencies, and show flattening at 150 MHz flux densities below 10 mJy associated with the rise of the low flux density star-forming galaxies and radio-quiet AGN