The branch of Differential geometry of differentiable manifolds is very vast and an interesting field of study. Some of the major works in this field have been done by S.I. Goldbarg, M.Okumara, S. Sasaki, S. Yamaguchi, S. Sato, S. Tachibana, K. Yano, R.S. Mishra, K.L. Duggal, M.D. Upadhyay and others. The object of the present book is to introduce the Ø - recurrent, Ø - birecurrent and Ø - multirecurrent Generalized Manifolds namely GF and HGF- Manifolds and study its various geometric properties with the existence by interesting examples. This book would be useful for researches and scholars engaged in research field of concerned subject.