Reddit mentions of A Mathematical Gift I, II, III: The Interplay Between Topology, Functions, Geometry, and Algebra (Mathematical World) (v. 1-3)

Check out this list. It includes most if not all books mentioned here.

From more to less advanced, generally:

• Geometry by Gray, Esplen, and Brannan
  
  
• The Infinite in the Finite
  
  
• A Geometrical Picture Book
  
  
• 99 Points of Intersection: Examples-Pictures-Proofs
  
  
• Lines and Curves: A Practical Geometry Handbook
  
  
• The Heart of Mathematics
  
  
• The Symmetries of Things
  
  
• A Mathematical Gift, 1: The Interplay Between Topology, Functions, Geometry, and Algebra (Mathematical World) (v. 1)
  
  A Mathematical Gift, II
  
  A Mathematical Gift, III: The Interplay Between Topology, Functions, Geometry, and Algebra (Mathematical World) (v. 3)
  
  Note the first three volumes are cheaper as a set.
  
  Intuitive Topology (Mathematical World, Vol 4)
  
  Groups and Symmetry: A Guide to Discovering Mathematics (Mathematical World, Vol. 5)
  
  Knots and Surfaces: A Guide to Discovering Mathematics (Mathematical World, Vol. 6)
  
  
• A Beginner's Guide to Constructing the Universe
  
  and 5 activity books in the same style
  
  
• Going beyond books, but visual, manipulative, and tactile, the Zome Tools

Here are some great books that I believe you may find helpful :)

• Elements of Algebra by Leonhard Euler
  
• Foundations of Mathematics by Ian Stewart
  
• Geometry Revisited by H. S. M. Coxeter
  
• Excursions in Calculus by Robert M. Young
  
• New Horizons in Geometry by Tom M. Apostol and Mamikon A. Mnatsakanian
  
• The Calculus Gallery: Masterpieces From Newton to Lebesgue by William Dunham
  
• A Primer of Real Functions by Ralph P. Boas
  
• Understanding Analysis by Stephen Abbot
  
• Chaos: Making a New Science by James Gleick
  
• Logic: An Introduction to Elementary Logic by Wilfred Hodges
  
  and last but definitely not least:
  
  
• A Mathematical Gift I, II, III by Kenji Ueno et al.
  
  Later on:
  
  
• Conceptual Mathematics: A First Introduction to Categories by F. William Lawvere
  
• Twelve Landmarks of Twentieth-Century Analysis by D. Choimet & H. Queffélec
  
• Theory of Complex Functions by Reinhold Remmert
  
• Algebraic Combinatorics. Walks, Trees, Tableaux & More by Richard P. Stanley