This paper introduces higher-order topological insulators (HOTIs), which are three-dimensional materials with insulating surfaces but protected gapless hinge states. The study extends the concept of topological insulators to systems where surface states are absent, but protected hinge states exist. Two types of HOTIs are discussed: (i) Chiral HOTIs protected by time-reversal and fourfold rotation symmetry, with chiral hinge modes and Z₂ classification, and (ii) Helical HOTIs protected by time-reversal and mirror symmetries, with Kramers pairs of hinge modes and Z classification. The paper provides topological invariants for both cases and demonstrates that materials such as SnTe and surface-modified Bi₂Te₁/₂, BiSe, and BiTe are helical HOTIs. It also proposes an experimental setup to detect hinge states in a topological SnTe coaxial cable. The study shows that the topological properties of HOTIs are protected by spatiotemporal symmetries, and the bulk-surface-hinge correspondence is established. The paper also discusses the implications of these findings for topological superconductors and other topological phases of matter.This paper introduces higher-order topological insulators (HOTIs), which are three-dimensional materials with insulating surfaces but protected gapless hinge states. The study extends the concept of topological insulators to systems where surface states are absent, but protected hinge states exist. Two types of HOTIs are discussed: (i) Chiral HOTIs protected by time-reversal and fourfold rotation symmetry, with chiral hinge modes and Z₂ classification, and (ii) Helical HOTIs protected by time-reversal and mirror symmetries, with Kramers pairs of hinge modes and Z classification. The paper provides topological invariants for both cases and demonstrates that materials such as SnTe and surface-modified Bi₂Te₁/₂, BiSe, and BiTe are helical HOTIs. It also proposes an experimental setup to detect hinge states in a topological SnTe coaxial cable. The study shows that the topological properties of HOTIs are protected by spatiotemporal symmetries, and the bulk-surface-hinge correspondence is established. The paper also discusses the implications of these findings for topological superconductors and other topological phases of matter.