The Atacama Large Millimeter Array, hereafter ALMA, is a large international telescope project which will be built over the next decade in northern Chile on a site at 5 km elevation. The site provides excellent atmospheric transmission in the millimeter and sub-millimeter wavelength ranges. The project consists of sixty-four 12-m antennas which can be placed on 250 different stations. These stations cover baselines up to 14 km. At the shortest planned wavelength, λ = 0.3 mm, and longest baseline, the angular resolution will be 0.005 arcsec. The receivers are superconducting (SIS) mixers, to provide the lowest possible receiver noise contribution. In the basic ALMA project the 4 highest priority receiver bands will be installed first (see Table 2). These will all have SIS mixers for both polarizations, each with a bandwidth of 8 GHz. A unique feature of ALMA is that this instrument will record both interferometric and total power data. Thus the complete flux density will be recovered. In the following, we present the status of the ALMA project as of end 2003 with a few comments about future developments in the project in Section 7.