This paper introduces a formal grammatical system called link grammar, which is used to parse English sentences. Link grammar is based on the principle of planarity, where arcs connecting words in a sentence do not cross. The system allows for efficient parsing of English sentences by encoding grammatical rules in a dictionary of linking requirements. Although link grammars have the same expressive power as context-free grammars, they are easier to use for encoding natural language grammars. The authors have developed a program for parsing sentences using link grammar and a dictionary for English. The program is written in C and is available online. The paper describes the workings of a link grammar for English, including the use of connectors, disjunctive form, and the algorithm for parsing. It also discusses the challenges of handling coordination phenomena, post-processing, and other linguistic features. The paper concludes with a discussion of the advantages of the link grammar system and its potential applications in natural language processing.This paper introduces a formal grammatical system called link grammar, which is used to parse English sentences. Link grammar is based on the principle of planarity, where arcs connecting words in a sentence do not cross. The system allows for efficient parsing of English sentences by encoding grammatical rules in a dictionary of linking requirements. Although link grammars have the same expressive power as context-free grammars, they are easier to use for encoding natural language grammars. The authors have developed a program for parsing sentences using link grammar and a dictionary for English. The program is written in C and is available online. The paper describes the workings of a link grammar for English, including the use of connectors, disjunctive form, and the algorithm for parsing. It also discusses the challenges of handling coordination phenomena, post-processing, and other linguistic features. The paper concludes with a discussion of the advantages of the link grammar system and its potential applications in natural language processing.