Anesthesia is considered as a process in which unconsciousness, muscle relaxation, and the reduction of sensitivity to painfull stimuli are occured. Ensuring patient’s safety during surgical operation and in the intensive Care Unit (ICU) is an important facor. Nevertheless, patient awareness during surgery or over dosing with anesthetic agents will be a common problem. In order to avoid these problems, accurate detection of depth of anesthesia (DOA) based on processing of physiological signals is a proper choice. Synaptic activity of neurons which are the main generators of electroencephalogram (EEG) signals is highly affected by various anesthetic drugs. Thus, in the recent years, a large focus was put on digital processing of EEG signals for estimating depth of anesthesia. In this thesis, the probable algorithm of the BIS monitor is analyzed and the efficiency of the spectral, bispectral and temporal parameters in estimating DOA is evaluated. In order to improve the accuracy of the algorthims, adaptive segmentation methods are used, too. Furthermore, the concepts such as Shannon entropy, Huffman coding, and approximate entropy which are extracted out of the information theory are studeied and their ability to estimating DOA is analyzed. In addition, Independent Component Analysis (ICA) and Principal Component Analysis (PCA) are reviewed, analysed, and used to assess a better estimator of DOA. Based on the chaos theory, fractal dimension of the EEG signal is measured and used for estimating DOA. The results are evaluated and compared via appropriate statistical analyzers. Results show the ability of spectral and bispectral parameters in predicting DOA. Also, the capability of the parameters (such as fractal dimention and approximate entropy) which are able to quantify the complexity of the EEG signal is shown. It should be mentioned that none of above algorthims could estimate the DOA in all of the drug regimens and groups, properly. Accordingly we conclude that, an ideal DOA monitor should use different signal processing algorithms and different adaptive segmentation methods and may use a combination of these policies in order to estimate the DOA more accurately.