Princeton Neuroscience Institute

Please find below definitions from Wikipedia of basic Neuroscience fields.

Cellular neuroscience is the study of neurons at a cellular level including morphology and physiological properties of single neurons. 

Cellular neuroscience. (2009, September 11). In Wikipedia, The Free Encyclopedia. Retrieved 20:05, October 22, 2009, from http://en.wikipedia.org/w/index.php?title=Cellular_neuroscience&oldid=313226294

Computational neuroscience is an interdisciplinary science that links the diverse fields of neuroscience, cognitive science, electrical engineering, computer science, physics and mathematics. Historically, the term was introduced by Eric L. Schwartz. The early historical roots of the field can be traced to the work of people such as Hodgkin & Huxley, Hubel & Wiesel, and David Marr, to name but a few. Hodgkin & Huxley developed the voltage clamp and created the first mathematical model of the action potential. Hubel & Wiesel discovered that neurons in primary visual cortex, the first cortical area to process information coming from the retina, have oriented receptive fields and are organized in columns.^{[ 2 ]} David Marr's work focused on the interactions between neurons, suggesting computational approaches to the study of how functional groups of neurons within the hippocampus and neocortex interact, store, process, and transmit information. Computational modeling of biophysically realistic neurons and dendrites began with the work of Wilfrid Rall, with the first multicompartmental model using cable theory.

Computational neuroscience is distinct from psychological connectionism and theories of learning from disciplines such as machine learning, neural networks and statistical learning theory in that it emphasizes descriptions of functional and biologically realistic neurons (and neural systems) and their physiology and dynamics. These models capture the essential features of the biological system at multiple spatial-temporal scales, from membrane currents, protein and chemical coupling to network oscillations, columnar and topographic architecture and learning and memory. These computational models are used to test hypotheses that can be directly verified by current or future biological experiments.

Computational neuroscience. (2009, October 22). In Wikipedia, The Free Encyclopedia. Retrieved 20:01, October 22, 2009, from http://en.wikipedia.org/w/index.php?title=Computational_neuroscience&oldid=321428565

Developmental neuroscience (also termed Neural development) describes the cellular and molecular mechanisms by which complex nervous systems emerge during embryonic development and throughout life. 

Neural development. (2009, September 5). In Wikipedia, The Free Encyclopedia. Retrieved 20:10, October 22, 2009, from http://en.wikipedia.org/w/index.php?title=Neural_development&oldid=312019875

Systems neuroscience is a subdiscipline of neuroscience which studies the function of neural circuits and systems, most commonly in awake, behaving intact organisms. It is an umbrella term, encompassing a number of areas of study concerned with how nerve cells behave when connected together to form neural networks: vision, for example, or voluntary movement. At this level of analysis, neuroscientists study how different neural circuits analyze sensory information, form perceptions of the external worlds, make decisions, and execute movements. Researchers concerned with systems neuroscience focus on the vast space that exists between molecular and cellular approaches to the brain and the study of high-level mental functions such as language, memory, and self-awareness (which are the purview of behavioral and cognitive neuroscience).  

Systems neuroscience. (2009, September 20). In Wikipedia, The Free Encyclopedia. Retrieved 20:11, October 22, 2009, from http://en.wikipedia.org/w/index.php?title=Systems_neuroscience&oldid=315024954