Quote by Matterwave
Kaluza was the one who proposed a fifth dimension on which the curvature gives you the Maxwell's equations. Klein later proposed a mechanism by which this fifth dimension could exist without us realizing it (compactification). Thus, this 5D GR+E&M theory is called "Kaluza Klein theory". String theory uses ideas from this (extra dimensions, and compactification), but is not the same as this.
I don't know what Weyl has to do with that...

Yes, checking the Elegant Universe book, it was Klein, not Weyl.
But what Weyl did was this
http://www.ams.org/notices/200607/feamarateck.pdf
"In a 1918 article Hermann Weyl tried to combine electromagnetism and gravity by requiring the theory to be invariant under a local scale change of the metric, i.e., gμν → gμν e^α(x), where x is a 4vector. This attempt was unsuccessful and was criticized by Einstein for being inconsistent with observed physical results. It predicted that a vector parallel transported from point p to q would have a length that was path dependent. Similarly, the time interval between ticks of a clock would also depend on the path on which the clock was transported.
The article did, however, introduce
• the term “gauge invariance”; his term was Eichinvarianz. It refers to invariance under his scale
change. The first use of “gauge invariance” in English3 was in Weyl’s translation4 of his famous
1929 paper.
• the geometric interpretation of electromagnetism.
• the beginnings of nonabelian gauge theory. The similarity of Weyl’s theory to nonabelian gauge theory is more striking in his 1929 paper."
Objections?