Final answer:
The Establishment Clause issues mainly concern the separation of church and state, such as prayer in schools and the endorsement of religion by public resources, balanced against individual rights to free exercise of religion.
Step-by-step explanation:
The Establishment Clause of the First Amendment presents several issues, particularly when it intersects with public education. One major focus has been prayer in school. The Supreme Court has held that while individuals have the freedom to exercise religion, public school-related activities cannot endorse religion.
This includes teacher-led prayers or ceremonies at school events that incorporate religious practices, as they may be seen as a governmental endorsement of religion, violating the Establishment Clause. Nonetheless, private, non-disruptive prayer by students remains permissible.
Furthermore, the Supreme Court established in Lemon v. Kurtzman a three-part test to determine if a law is constitutional under the Establishment Clause: it must have a secular purpose, not advance or inhibit religion, and avoid excessive entanglement between government and religion.