Image segmentation is a fundamental task in image processing and computer vision. Applications of image segmentation are urgent important, e.g. Robot Vision, Medical Imaging, Radar Imaging, Sonar Imaging, Remote Sensing, Astronomy, Traffic, Defense, Mining, Object Tracking and Detection, Finger Print Detection and so on. The main aim of image segmentation is to extract meaningful objects from a given image. For example, a boy of just three years can see/detect/locate a pen on a table, as he is naturally equipped with image segmentation power, robots can not do it, until they use image segmentation algorithms. To perform an image segmentation task, several techniques have been developed. One of simple and flexible technique is discussed in this book from basics. This technique is known as variational modeling for image segmentation. This technique can help readers to work in other image processing tasks as well, such as image denoising, image inpainting, image debluring, image recognition, image registration.