This thesis aims to develop the theoretical and experimental means to study the nature of the neural networks of the nervous system. The most important parameters in a neural network are its synaptic connectivities (connection weights). Once the unknown connectivities in the nervous system are discovered, appropriate neural network models can be designed and used to mimic their action. To study the functional connectivity, reliable recording and identification of the simultaneous activities of a group of neurons is essential. In the first part of this thesis, a system for neural spike detection and classification is presented, which does not require a priori assumptions about spike shape or timing. The system consists of two subsystems. The learning subsystem, comprising a Haar transform detection scheme, a feature learning phase and a template learning phase, extracts templates for each separable spike class. The real-time detection and classification subsystem identifies spikes in the noisy neural trace and sorts them into classes, according to the templates and the statistics of the background noise. Three fast algorithms are proposed for the real-time sorting subsystem, and comparisons are made among different schemes. Performance of the system is illustrated by using it to classify spike in segments of neural activity recorded extracellularly from monkey motor cortex and from guinea pig and ferret auditory cortices. The system is implemented without human supervision and therefore is suitable for real-time multichannel recording. In the second part, analytical and experimental methods are provided for estimating synaptic connectivities from simultaneous recordings of multiple neurons (after separation). The results are based on detailed, yet flexible neuron models in which spike trains are modeled as general doubly stochastic point processes. The expressions derived can be used with nonstationary or stationary records, and can be readily extended from pairwise to multineuron estimates. Furthermore, we show analytically how the estimates are improved as more neurons are sampled, and derive the appropriate normalizations to eliminate stimulus-related correlations. Finally, we illustrate the use and interpretation of the analytical expressions on simulated spike trains and neural networks, and give explicit confidence measures on the estimates.