Musical improvisation is an art that was practiced by the majority of keyboard masters and pedagogues of the past. Johann Sebastian Bach, Ludwig van Beethoven, Franz Liszt, and many others improvised during public performance and encouraged improvisation among their students. In today's music world, however, classical pianists are rarely comfortable improvising; as a result, they avoid teaching improvisatory skills at all levels, including in higher education facilities. Logically, if the teacher is not comfortable with improvisation, no attempt should be made to teach the art. Improvisation, however, is still a useful skill in the twenty-first century and should become a regular part of a classical pianist's training. This study primarily provides methods through which classical pianists can learn the fundamentals of improvisation and acquire the ability to teach improvisation to their students. These methods are useful to both student and teacher. Classical pianists must learn the foundations of improvisation in order to prevent the loss of an art that was once valuable to the historical masters of the keyboard and can be equally so to pianists today.