Are there lunar granites? 
Does the moon have a crust like the Earth?

Danilo Anton

It seems that the phase change that happened in the upper mantle of the Earth, happened with much less frequency in the moon. There are few lunar granites and they include diorites, monzodiorites, and granophyres. Mineralogically they are composed of quartz, plagioclase, orthoclase or alkali feldspar, rare mafics (pyroxene), and rare zircon. 

There is very little quartz in the moon surface showing that the original composition of the moon interior is not identical to the one we found on Earth.

The alkali feldspar may have unusual compositions unlike any terrestrial feldspar, and they are often Ba-rich. These rocks apparently form by the extreme fractional crystallization of magnesian suite or alkali suite magmas, although liquid immiscibility may also play a role. U-Pb date of zircons from these rocks and from lunar soils have ages of 4.1-4.4 Ga, more or less the same as the magnesian suite and alkali suite rocks. In the 1960s, NASA researcher John A. O'Keefe and others linked lunar granites with tektites found on Earth although many researchers refuted these claims. According to one study, a portion of lunar sample 12013 has a chemistry that closely resembles javanite tektites found on Earth.

(partially taken from wikipedia)