Network science has become increasingly popular in the cognitive sciences, including linguistics. This book is the first to explore lexical networks in learners of English as a second language, focusing on the relationships between phonological word forms in the mental lexicon. It highlights the contributions that network science can make to the study of lexical organization of second languages.Within the theoretical framework of evolving networks, lexical learning is seen as a process of network growth. The lexicon is modeled as a growing phonological network that increases in size as language users advance through second language proficiency stages. This allows the analysis of specific growth algorithms (such as preferential attachment) that can account for observed mechanisms of lexical acquisition. Empirical models of evolving lexical networks can help elucidate the structural changes occurring as the second language lexicon expands.