Steganography is the study of hiding information so that its presence is unknown to anybody except the person who hid it. This differs from cryptography which aims to make a message unintelligible to anybody who does not know the secret key to decrypt a message. This thesis first provides a brief description of previous work that has been done using the singular value decomposition for steganography and a new algorithm to use the singular value decomposition for steganography in images is presented. The algorithm is then optimized to reduce error and maintain visual fidelity in the images to which it is applied. Finally, more ideas for future research involving this algorithm are discussed.