This book is a contribution to the ongoing research in the design of hard disk encryption, an important field used to protect the confidentiality of data in the disk. We focus on tweakable ciphers as these appear to offer the best combination of security and performance. In this book, we highlight the research to date in the area of disk encryption and propose a novel narrow-block disk encryption mode of operation with compression of data first. This is the Tweaked Block Chaining (TBC) mode using Xor-Encrypt-Xor (XEX) to inherit from its security and high performance and use CBC like operations to gain the error propagation property. Here we use "LZW 15-bit Variable Rate Encoder" for the compression of data. We also apply multiplication and exponential in the finite field GF (2^128). Here we use Ciphertext Stealing when data size is not multiple of 16 bytes. Our hope is to generate a disk encryption scheme that will provide high throughput, faster, memory saving and better resistant to the known attacks.