Fingering
You usually won't go wrong by using the fingering marked on the music. Or, rather, if you don't follow the indicated fingering, you will probably get into a lot of trouble. Except in beginners' books, the basic fingerings are usually obvious and are not indicated in music scores. Some indicated fingerings may feel awkward at first, but it is there for a reason. This reason often does not become obvious until you get up to speed and/or you play HT. For beginners, following the indicated fingering is an educational experience for learning the most common fingerings. Another advantage of using the indicated fingering is that you will always use the same one. Not having a fixed fingering will greatly slow down the learning process and give you trouble later, even after you have learned the piece well. If you do change the fingering, make sure that you always stick to the new one. It is a good idea to mark the change on the music; it can be very annoying to come back to this music months later and not remember that nice fingering you had previously worked out.
However, not all suggested fingerings on the music score are appropriate for everyone. You may have large or small hands. You may have gotten used to a different fingering because of the way you learned. You might have a different skill set; e.g., you might be a better triller using 1,3 than 2,3. Music from different publishers may have different fingerings. For advanced players, the fingering can have a profound influence on the musical effect you want to project. Fortunately, the methods of this book are well suited to quickly changing fingerings. Part of the "explorations" alluded to above involve making sure that the fingering is optimized. Once you have become familiar with these methods, you will be able to change fingering very quickly. Make all the changes before you start HT practice because once fingerings are incorporated into HT play, they become very difficult to change. On the other hand, some fingerings are easy HS but become difficult HT, so it pays to check them HT before permanently accepting any changes. Everybody should memorize the fingerings for all the scales and arpeggios (section III.5), as well as the chromatic scale, and to practice them until they become ingrained habits.