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

Danilo Anton

In the Earth geology it is observed that the rocks that are more abundant almost everywhere are granites, understanding as granites those rocks mainly composed of feldspar and quartz, plus other secondary minerals. IN some cases the rocks are composed of grains (crystals about 0.5  to 3 cm long) and in other cases the crystals are very small, as is the case with some volcanic rocks, such as rhyolites or trachytes. In those cases the composition remains also granitic.

It is very strange that lunar rocks do not have quartz as a mineral, and therefore, granites are practically absent in the moon surface.

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.

Sources of moon rocks
Moon rocks on Earth come from three sources: those collected by the United States Apollo program crewed lunar landings from 1969 to 1972; samples returned by three Soviet Luna programme uncrewed probes in the 1970s; and rocks that were ejected naturally from the lunar surface before falling to Earth as lunar meteorites. The Apollo missions collected 2,200 samples weighing 382 kilograms (842 lb). Three Luna spacecraft returned with 301 grams (10.6 oz) of samples. More than 370 lunar meteorites have been collected on Earth, representing more than 30 different meteorite finds (no falls), with a total mass of over 190 kilograms (420 lb). Some were discovered by scientific teams (such as ANSMET) searching for meteorites in Antarctica, with most of the remainder discovered by collectors in the desert regions of northern Africa and Oman.

(partially taken from wikipedia)