Knowledge of the relationship between functional brain activity and its anatomical source is vital in many clinical situations. A multidisciplinary research approach is necessary to enhance understanding of the basic mechanisms of normal and pathological brain functions. Although functional neuroimaging techniques such as functional Magnetic Resonance Imaging (fMRI) facilitate noninvasive access to the active brain, the low temporal resolution necessitates using alternative techniques to study brain dynamics. Electroencephalography (EEG) is a non-invasive method for acquiring neural information with high temporal resolution which measures electric potential over the scalp corresponding to neural activity. EEG source localization (ESL) is a technique applied to EEG to localize the sources of the measured potentials. This technique has been applied to EEG in adults in the studies of physiological, psychological, pathological, and functional brain abnormalities such as tumours and epilepsies. There are indications of the early brain developmental roots of specific abnormalities such as autism, Williams syndrome and schizophrenia that are observed in certain developmental and neuropsychiatric disorders. However, these observations have been performed only in adults. Indeed, despite the necessity of research in neonatal brain functional analysis for medical care of preterm and ill infants, there is limited research in neonatal ESL due in part to limitations in acquiring the relevant parameters of the neonatal head. The overall objective of this thesis is to improve neonatal health care through enhancing non-invasive neonatal brain monitoring by developments in neonatal ESL. The accuracy of neonatal ESL is critically dependant on the quality of the head model whose main components, conductivity, thickness, and homogeneity of different layers have not been established. The number of electrodes needed to capture neonatal EEG in full spatial detail is another missing parameter of importance in extracting information about functional brain activity from neonatal scalp recordings. The last step to achieve this objective, neonatal ESL development, is proposing and applying an accurate algorithm to estimate neural currents from scalp potentials, i.e., to solve the inverse EEG problem. This thesis proposes methodologies for estimating the required neonatal head model parameters and then solves the inverse EEG problem in newborns. This has been completed in three steps by: (i) estimating the source depth and spatial resolution of neonatal EEG, (ii) estimating appropriate head model conductivity values including the effect of fontanelles on neonatal skull conductivity, and (iii) fitting an inverse solution to the neonatal ESL problem. Solving EEG inverse problem in this thesis refers to computing the inverse solution in a particular case. After completing these steps, the procedure is validated and evaluated through simulated and real EEG datasets. Parameters such as neonatal skull conductivity cannot be directly calculated in n...