We introduce a new notion called ({\cal Q})-secure pseudorandom isometries (PRI). A pseudorandom isometry is an efficient quantum circuit that maps an (n)-qubit state to an ((n+m))-qubit state in an isometric manner. In terms of security, we require that the output of a (q)-fold PRI on (\rho), for ( \rho \in {\cal Q}), for any polynomial (q), should be computationally indistinguishable from the output of a (q)-fold Haar isometry on (\rho). By fine-tuning ({\cal Q}), we recover many existing notions of pseudorandomness. We present a construction of PRIs and assuming post-quantum one-way functions, we prove the security of ({\cal Q})-secure pseudorandom isometries (PRI) for different interesting settings of ({\cal Q}). We also demonstrate many cryptographic applications of PRIs, including, length extension theorems for quantum pseudorandomness notions, message authentication schemes for quantum states, multi-copy secure public and private encryption schemes, and succinct quantum commitments.