Texture analysis is an extremely active and useful area of research. In texture analysis the invariance to rotation, scale and translation are the most typical requirements. Moreover, gray-scale invariance is another important issue. It arises due to the reason that a texture may be subject to different levels of illumination. The purpose of this study is to investigate some inexpensive approaches that are rotation and gray scale invariant and to large extent translation invariant as well. There are three different types of approaches, which have been addressed in this dissertation. In the first approach, we have done texture analysis using Radon Transform (RT) based Hidden Markov Model (HMM). We have introduced three different ways to extract feature vectors using RT. All three give rotation invariant features, while the last one gives rotation, as well as, gray scale invariant features. The textures in this case have been taken from Brodatz album. Due to the inherent property of the RT, we are able to capture the directional features of a certain texture having arbitrary orientation. This set of directional features is used for training of an HMM specifically for that particular texture. Once all the HMMs have been trained, the testing is carried out by using any one of these textures at random with arbitrary orientation. The second approach is somewhat similar to the above one except that the modified or Differential Radon Transform (DRT) has been used instead of the ordinary RT. Hence, we are able to capture the features which are not only rotation but are also gray scale invariant. The reason for the later property is that, unlike the ordinary RT, the DRT is based on the differences between adjacent pixels instead of summing up the pixel values. These features have been used for training of HMMs, one for each texture, and finally testing is carried out. Similar experimentation has been done to extract features using both RT and DRT to give low pass and high pass features. The training and testing process using HMM has been done in a similar manner as above. The third approach is quite different from the above two approaches. In this approach, some principal direction of a texture is defined. Once this direction is estimated, discrete wavelet transform is applied in that particular direction to extract features. These features are then used for classification by k-nearest neighbor classifier. There are two definitions of principal direction, which have been proposed in the dissertation. In case of vthe first definition, Principal Component Analysis (PCA) has been used to estimate this principal direction. In the case of second definition, the direction has been found out by using DRT. This scheme is computationally lighter compared to the previous one. However, the third approach is limited to anisotrpic textures only unlike the previous method Considering the percentage of correct classification as figure of merit, we have carried out the performance evaluation of the above three approaches. The average result has been found to be 95% approximately and the best result has been close to 100%.