Short answers, pulled from the story.
Petrology is the branch of geology that studies rocks, including their mineralogy, composition, texture, structure, and the conditions under which they form. Lithology focuses on macroscopic hand-sample or outcrop-scale description of rocks, while petrography, a specialty within petrology, deals with microscopic details.
The three branches of petrology are igneous petrology, metamorphic petrology, and sedimentary petrology, each corresponding to one of the three main rock types. A fourth area, experimental petrology, uses high-pressure and high-temperature apparatus to study geochemistry and phase relations.
Igneous petrology studies rocks that have crystallized from molten rock or magma, such as granite and basalt. It covers both volcanic rocks and plutonic rocks.
A protolith is the original rock before it undergoes metamorphic change due to pressure, temperature, or both. The protolith can be of any rock type; for example, limestone becomes marble and shale becomes slate.
Experimental petrology uses high-pressure, high-temperature apparatus to study rocks that are otherwise inaccessible, such as those in the Earth's lower mantle and the mantles of other terrestrial planets and the Moon. No direct surface samples of these materials exist, making laboratory experiments one of the prime sources of information about them.
In the petroleum industry, petrology informs mud logging, the graphic representation of geological formations drilled through and recorded on a mud log. Cuttings from the borehole are examined, typically under a ten-times magnification microscope, and tested chemically to identify the formations being drilled.