We investigate the geometric and topological properties of 2-knots embedded in a four-dimensional real space. Starting from the fundamental group of the complement of an embedded 2-sphere in \mathbb{R}^4, we provide an intuitive geometric interpretation and analyze how local immersion structures of surfaces influence this group. This viewpoint is extended to complements of general 2-knots, where we establish its invariance under Reidemeister moves (R-moves), illustrated by the spun trefoil knot. Emphasis is placed on the geometric meaning of algebraic invariants: we examine the interplay between 2-knot diagrams, the Alexander polynomial, and the Alexander matrix, interpreting the latter via the associated chain complex. We also study the geometric implications of relator substitutions, clarify the relationship between the Burau representation and the Alexander matrix, and outline potential applications of these structures in both mathematics and applied contexts. The following summarizes my major research outcomes and contributions: 1.Provided a geometric interpretation of the properties of the fundamental group of knot and 2-knot complements. 2.Derived a skein relation formulation of the Alexander polynomial for 2-knots. 3.Established a connection between the Artin representation of braid groups and the Alexander matrix. 4.Investigated the structure of 2-knot Alexander invariants and related invariants from a matrix-theoretic perspective. 5.Explored practical applications of knot theory, with cryptography as a case study.