A review of the most significant recent works by K.V. Kholshevnikov on analytical celestial mechanics is presented, which expands on the 21st century segment of Part II of the review of astronomical research conducted at St. Petersburg University in this field. The intrinsic connection of analytical celestial mechanics with mathematical methods is emphasized. The potential of this direction in modern fundamental and applied astronomical research is demonstrated. Some other aspects of Kholshevnikov’s activity as an astronomer and mathematician, and a devotee of science and education, are also noted.