Paleobiology (sometimes spelled palaeobiology) is a growing and comparatively new discipline which combines the methods and findings of the natural science biology with the methods and findings of the earth science paleontology. It is occasionally referred to as "geobiology."
Paleobiological or paleobiologic research uses biological field research of current biota and of fossils millions of years old to answer questions about the molecular evolution and the evolutionary history of life. In this scientific quest, macrofossils, microfossils and trace fossils are typically analyzed. However, the 21st-century biochemical analysis of D.N.A. and R.N.A. samples offers much promise, as does the biometric construction of phylogenetic trees.
Some of the more-pertinent paleobiologic journals are: Biology and Geology; Historical Biology; Palaios; the journal Palaeogeography, Palaeoclimatology, Palaeoecology; Paleobiology; and Paleooceanography.
An investigator in this field is known as a paleobiologist. Some of the more important research areas of paleobiologists are listed below, along with various internal linkages:
examining past ecosystems, climates, and geographies so as to better comprehend prehistoric life.
analyzing the post-mortem history (for example, decay and decomposition) of an individual organism in order to gain insight on the behavior, death and environment of the fossilized organism.
analyzing the tracks, borings, trails, burrows, impressions, and other trace fossils left by ancient organisms in order to gain insight into their behavior and ecology.
studying long-term secular changes, as well as the (short-term) bed-by-bed sequence of changes, in organismal characteristics and behaviors. See also stratification, sedimentary rocks and the geologic time scale.
The founder or "father" of modern paleobiology is said to be Baron Franz Nopcsa (1877 to 1933), a turn-of-the-century Balkan scientist. He is also known as Baron Nopcsa, Ferenc Nopcsa, and Franz Nopcsa von Felsö-Szilvás. He initially termed the discipline "paleophysiology."
However, credit for coining the word paleobiology itself should go to Professor Charles Schuchert. He proposed the term in 1904 so as to initiate "a broad new science" joining "traditional paleontology with the evidence and insights of geology and isotopic chemistry." 
On the other hand, Charles Doolittle Walcott, a Smithsonian adventurer, has been cited as the "founder of Precambrian paleobiology." Although best-known as the discoverer of the mid-Cambrian Burgess shale animal fossils, in 1883 this American curator found the "first Precambrian fossil cells known to science" -- a stromatolite reef then known as Cryptozoonalgae. In 1899 he discovered the first acritarch fossil cells, a Precambrian algal phytoplankton he named Chuaria. Lastly, in 1914, Walcott reported "minute cells and chains of cell-like bodies" belonging to Precambrian purple bacteria. 
Later 20th-century paleobiologists have also figured prominently in finding Archaean and Proterozoic eon microfossils: In 1954, Stanley A. Tyler and Elso S. Barghoorn described 2.1 billion-year-old cyanobacteria and fungi-like microflora at their Gunflint chert fossil site. Eleven years later, Barghoorn and J. William Schopf reported finely-preserved Precambrian microflora at their Bitter springs site. 
Finally, in 1993, Schopf discovered O2-producing blue-green bacteria at his 3.5 billion-year-old Apex chert site in Pilbara Craton, Marble Bar, in the northwestern part of Western Australia. So paleobiologists were at last honing in on the origins of the Precambrian "Oxygen catastrophe." 
Derek E.G. Briggs and Peter R. Crowther, eds. (2003). Palaeobiology II. Malden, Massachusetts: Blackwell Publishing. ISBN 0-632-05147-7 and ISBN 0-632-05149-3. The second edition of an acclaimed British textbook.
Robert L. Carroll (1998). Patterns and Processes of Vertebrate Evolution. Cambridge Paleobiology Series. Cambridge, England: Cambridge University Press. ISBN 9788521478090 and ISBN 052147809X. Applies paleobiology to the adaptive radiation of fishes and quadrapeds.
Matthew T. Carrano, Timothy Gaudin, Richard Blob, and John Wible, eds. (2006). Amniote Paleobiology: Perspectives on the Evolution of Mammals, Birds and Reptiles. Chicago: University of Chicago Press. ISBN 0226094782 and ISBN 978-0226094786. This new book describes paleobiological research into land vertebrates of the Mesozoic and Cenozoic eras.
Robert B. Eckhardt (2000). Human Paleobiology. Cambridge Studies in Biology and Evolutionary Anthropology. Cambridge, England: Cambridge University Press. ISBN 0521451604 and ISBN 9780521451604. This book connects paleoanthropology and archeology to the field of paleobiology.
Douglas H. Erwin (2006). Extinction: How Life on Earth Nearly Ended 250 Million Years Ago. Princeton: Princeton University Press. ISBN 978-0-691-00524-9. An investigation by a paleobiologist into the many theories as to what happened during the catastrophic Permian-Triasssic transition.
Brian Keith Hall and Wendy M. Olson, eds. (2003). Keywords and Concepts in Evolutionary Biology. Cambridge, Massachusetts: Harvard University Press. ISBN 0674009045 and ISBN 9780674009042.
David Jablonski, Douglas H. Erwin, and Jere H. Lipps (1996). Evolutionary Paleobiology. Chicago: University of Chicago Press, 492 pages. ISBN 0226389111 and ISBN 0226389138. A fine American textbook.
Masatoshi Nei and Sudhir Kumar (2000). Molecular Evolution and Phylogenetics. Oxford, England: Oxford University Press. ISBN 0195135857 and ISBN 978-0195-135855. This text links DNA/RNA analysis to the evolutionary "tree of life" in paleobiology.
Donald R. Prothero (2004). Bringing Fossils to Life: An Introduction to Paleobiology. New York: McGraw Hill. ISBN 0073661708 and ISBN 978-007366-1704. An acclaimed book for the novice fossil-hunter and young adults.
Mark Ridley, ed. (2004). Evolution. Oxford, England: Oxford University Press. ISBN 0199267944 and ISBN 9781-405-103459. An anthology of analytical studies in paleobiology.
Raymond Rogers, David Eberth, and Tony Fiorillo (2007). Bonebeds: Genesis, Analysis and Paleobiological Significance. Chicago: University of Chicago Press. ISBN 0226723704 and ISBN 9780226723709. A new book regarding the fossils of vertebrates, especially tetrapods on land during the Mesozoic and Cenozoic eras.
Thomas J. M. Schopf, ed. (1972). Models in Paleobiology. San Francisco: Freeman, Cooper. ISBN 0877353256 and ISBN 978-0877353256. A much-cited, seminal classic in the field discussing methodology and quantitative analysis.
Thomas J.M. Schopf (1980). Paleoceanography. Cambridge, Massachusetts: Harvard University Press. ISBN 0674652150 and ISBN 9780674652156. A later book by the noted paleobiologist. This text discusses ancient marine ecology.
J. William Schopf (2001). Cradle of Life: The Discovery of Earth's Earliest Fossils. Princeton: Princeton University Press. ISBN 0691088640. The use of biochemical and ultramicroscopic analysis to analyze microfossils of bacteria and archaea.
Paul Selden and John Nudds (2005). Evolution of Fossil Ecosystems. Chicago: University of Chicago Press. ISBN 978-02267-46418 and ISBN 022-6746410. A recent analysis and discussion of paleoecology.
Paul Tasch (1980). Paleobiology of the Invertebrates. New York: Wiley. ISBN 0471-052728 and ISBN 9780471-052722. Applies statistics to the evolution of sponges, cnidarians, worms, brachiopods, bryozoa, mollusks, and arthropods.
Shuhai Xiao and Alan J. Kaufman, eds. (2006). Neoproterozoic Geobiology and Paleobiology. New York: Springer Science+Business Media. ISBN 978-1-4020-5201-9. This new book describes research into the fossils of the earliest multicellular animals and plants, especially the Ediacaran period invertebrates and algae.
Bernard Ziegler and R. O. Muir (1983). Introduction to Palaeobiology. Chichester, England: E. Horwood. ISBN 0470275529 and ISBN 9780470275528. A classic, British introductory textbook.