A principle (in the usual meaning of the word) is a formulation regarded as enduringly true and which is a basis for thought or action. E.g., the principles of liberty, expressed in various ways in the U.S. Constitution, including the Bill of Rights. "Principle" is always used as a noun (although the derivative "principled", meaning "possessing principles", is an adjective).
Occasionally we see "principle" used in an unusual way, e.g., the title to a song by Enigma, "The Principles of Lust" ("are easy to understand ..."). Lust not being a reasonable (but rather an emotional) thing, it is here juxtaposed with the idea of principles for its dissonant, but not displeasing, effect.
"Principal", as a noun, is used in the U.S. to mean the chief administrator of a school (equivalent to "headmaster" in British schools). As an adjective, "principal" means "foremost, first, primary, main", as in "the principal reason I am here is ..." or "the principal cause of this phenomenon is ..." "Principal" can also be used as a noun to mean "the principal people, organizations, etc.", as in "the principals in the deal backed out as soon as ..."
It is not uncommon for "principal" to be misspelt as "principle". We find this error in an article in Penthouse magazine containing the sentence:
State Attorney General Bryant, in a 1991 letter to the office of Lawrence
Walsh, the independent counsel in the Iran-Contra investigation, wondered
"why no one was prosecuted in Arkansas despite a mountain of evidence
that [Barry] Seal [a cocaine smuggler working for the CIA] was using Arkansas as
his principle staging area during the years 1982 through 1985." (The Crimes of Mena)
This should have been: "... using Arkansas as his principal staging area ..."
Another meaning of "principal" is "money loaned or invested", and interest is paid on the principal. One also sees this misspelled, as in:
The culmination of decades of accumulated overspending by the [U.S.] government
has created an aggregate debt for the United States federal and state governments of
$14 trillion dollars. That's fourteen million million dollars. Or, to put it in
a more personal scale, more than $48,000 for every single living human being in
the United States, plus the accumulating interest.
The interest on that government debt now exceeds all the personal income tax collected by that government. That means that the government isn't keeping up with the interest
on the debt, let alone able to pay down the principle.
Should be "principal". Tough luck about those Americans, though. What was that about chickens coming home to roost? The chickens in this case being votes cast in federal and state elections in the last quarter-century.