College of Education for Pure Sciences, University of Babylon discussed a Ph.D.  thesis on some approaches to improving the reliability of complex networks by the postgraduate student, Mr. Fouad Hamza Abdul Nasser. The thesis highlighted mathematical models in the reliability of networks and the use of some known methods to calculate the reliability of complex networks as an application of statement theory and probability theory. The thesis aimed at using of a mathematical method to calculate the short paths and minimum segments of the network based on the algebra of matrices and implementing of some methods to obtain the reliability limits. The thesis demonstrated the short paths method, the minimal block method, parallel element reduction and delta-star transformation method, as well as using of some techniques for calculating the shortened network reliability assignment such as the exponential assignment technique and the Air Radio approach method.