This research monograph has the following main theme. Given an interpolation function, which is supposed to determine an estimate of the unknown signal value, the reader can use the traditional approach (traditional interpolation function) to estimate the numerical value of the signal. Alternatively, the reader can follow the theoretical developments offered in the book and so design, on the basis of the unified theory described in the book, three new interpolation functions with improved approximation capabilities. That means, that under the unified theory, the book offers three new classes of interpolation functions with improved approximation capabilities of the true and unknown signal to estimate. These works were published in the year 2011 and submitted for peer review and they are now presented to the public through this new publication. There are likely to be three main types of readership of this research monograph. The primary readership is composed of users of libraries which may adopt the book as reference. The secondary readership is composed of the population of instructors/professors of a course in one of applied mathematics, signal-image interpolation, signal-image processing, biomedical imaging and/or biomedical engineering academic disciplines. In such case, the book can be used as an additional educational resource to be available both to undergraduate and graduate students, in order to assign homework and/or projects to be included in the coursework. The tertiary readership is composed of apprentices and/or passionate of math. In such case, the book would be used to employ time while following the desire of intellectual enrichment. The apprentices and/or passionate of math would study the methodology of the unified theory, would apply the unified theory such to design new interpolation functions, and should there be the desire of furthering the interest, the apprentice and/or passionate would proceed further to the analysis of the results, and possibly into the discussion and the dissemination of the knowledge made out of this book.