James Hutton is often viewed as the first modern geologist. In 1785 he presented a paper entitled Theory of the Earth to the Royal Society of Edinburgh. In his paper, he explained his theory that the Earth must be much older than had previously been supposed, in order to allow enough time for mountains to be eroded, and for the sediment to form new rocks at the bottom of the sea, which were then raised up to dry land.
Followers of Hutton were known as plutonists because they believed that some rocks were formed by vulcanism which is the deposition of lava from volcanoes, as opposed to the neptunists, who believed that all rocks had settled out of a large ocean whose level gradually dropped over time.
Sir Charles Lyell first published his famous book, Principles of Geology, in 1830 and continued to publish new revisions until he died in 1875. He successfully promoted the doctrine of uniformitarianism. This theory states that slow geological processes occurred throughout the earth's history, and are still occurring today. In contrast, catastrophism is the theory that Earth's features formed in single, catastrophic events and remained unchanged thereafter. (Hutton believed in uniformitarianism, but the idea was not widely accepted at the time.)
There are many different fields within the discipline of Geology, and it would be hard to list all of them. Some include, however, Hydrogeology (or Geohydrology), Petroleum geology, Soil science, Climatology, Biogeology. Subdisciplines within geology proper include structural geology, sedimentology and stratigraphy (Sed/Strat), mineralogy (study of minerals), petrology (study of rocks), geomorphology (study of landforms), seismology (also a field in geophysics). There is also engineering geology, which supports civil engineering, especially geotechnical engineering, and geological engineering. The difference between geological engineering and engineering geology is real: geological engineers are licensed as engineers, engineering geologists are licensed as geologists.
James Hutton's Theory of the Earth: http://www.mala.bc.ca/~johnstoi/essays/Hutton.htm