You may find this brief summary of a/the leading contemporary model of intelligence to be of value:
http://www.iapsych.com/chcv2.pdfThough many of the lower order abilities are more conceptual than empirical, the broad abilities in this modified Cattell-Horn-Carroll model, in the top row, are largely supported by factor analytic research.
Another leading theory is Robert Sternberg's triarchic/successful intelligence (there is a much larger body of research, but this one is freely downloadable):
http://www.psicorip.org/Resumos/PerP/RIP/RIP036a0/RIP03921.pdfSome data supports this, mainly that students identified as having a preference for one of the three domains of intelligence (analytical, practical, creative) are more successful when instruction in a skill or concept includes their preferred domain for at least one component of the instructional set.