Biologically there is only one homo sapien
Differences in skin color, hair texture, nose width, etc. are such minor variants that they are not genetically significant and do not constitute different races.
Socially there are an almost infinite number of races and the debate will rage on until society becomes so mixed and homogenized as to render all classifications based on appearance as pointless.
Social scientists have claimed as few as three distinct races (caucasoid, mongoloid, negroid), to as many as several hundred based upon mixtures of different cultures. In our current age, race is primarily associated with skin color, but depending on who we are at war with this week, we make further race classifications to either fit our prejudice or to villify someone who disagrees with our political ideology.
Like liberal, conservative, socialist, fascist, marxist and a host of other words, we have so misused the term racist as to render it almost useless as a viable English language word.