This article proposes methodologies for developing intercultural competence, defined as the ability to constructively engage with cultures different from one's own. The research is practically oriented, with the methodologies applied by the author during a series of English language classes conducted at students' request outside of regular class hours. The course introduces students to significant artistic works from English-speaking cultures, focusing on issues such as: 1. the formation of universally significant values; 2. the development of abstract thinking for understanding cultural context; 3. a systemic perception of the world and its connection to ethics. Thematically, the modules address issues of humanism (using works by E. Hemingway), spiritual searching (W. Shakespeare and his contemporary reinterpretations), and absurdity in art (S. Beckett). The experience of conducting the course demonstrates that the issues raised meet the needs of students.