It took a very long time to write this book, especially to bring it to a relatively consistent and complete form. The journey of the reader to these final pages was also not easy and straightforward. What are your feelings after getting through the jungle of more than 1300 many-storeyed formulas? Perhaps, twofold. At first – relief and satisfaction: it is all over now, I made it! But secondly – are all these formulas correct? The answer is not so simple. I tried to do my utmost to be able to answer ‘yes’: compared with the original papers, deduced some of them again, checked numerically, looked for special cases, symmetry properties, etc. But I cannot assert that absolutely all signs, phases, indices, etc. are correct. Therefore, if you intend to do some serious research starting with one or other formula from the book, it is worthwhile carrying out additional checks, making use of one of the above mentioned methods.

Not all aspects of the theory are dealt with in equal depth. Some are just mentioned, some even omitted. For example, the method of effective (equivalent) operators deserves mentioning. It allows one to take into account the main part of relativistic effects but at the same time to preserve the LS coupling used for classification of the energy spectra of the atoms or ions considered.