Could anyone cite or give a source for a definition and an explanation of the term, "anathema"?  What happens when a pope, a bishop, or a priest incurs anathema?  What are the ramifications in the material realm?  How serious is it?  Is it contagious?  If Pope Paul VI created new rites of sacraments against Canon XIII of the Seventh Session of the Council of Trent, is participation in such rites under anathema also?

Thank you Ladislaus!

Douay-Rheims Bible
But though we, or an angel from heaven, preach a gospel to you besides that which we have preached to you, let him be anathema.


Galatians 1:8

Dear Viva Cristo Rey,
What did St. Paul mean when he commanded, "...let him be anathema"?  Who do you go to?  What are we supposed to do?

It used to be men would stand up against perversion.

Now society accepts evil as good and good is evil. 

Douay-Rheims Bible
Woe to you that call evil good, and good evil: that put darkness for light, and light for darkness: that put bitter for sweet, and sweet for bitter. 
Isaiah 

Dear Ladislaus,
Is there any theological treatise concerning "anathema" and its practical application?  Thank you!

I have not seen any, but that Catholic Encyclopedia article has a very lengthy treatment of the subject, and lists the following as its "Sources".

VIGOUROUX in Dict. de la Bible, s.v. Anethème; VACANT in Dict. de théol. cath., s.v. Anathème; VON SCHERER in Kirchenlex., 2d ed., I, 794-798; BENEDICT XIV, De Synodo Dioecesanâ, x, i.

Dear Ladislaus,
Is there any theological treatise concerning "anathema" and its practical application?  Thank you!

Not sure why you need anymore than what is explained in great detail in Catholic Encyclopedia, which sums up quite nicely the history of the term and the current theological consensus:

Anathema remains a major excommunication which is to be promulgated with great solemnity. A formula for this ceremony was drawn up by Pope Zachary (741-52) in the chapter Debent duodecim sacerdotes, Cause xi, quest. iii. The Roman Pontifical reproduces it in the chapter Ordo excommunicandi et absolvendi, distinguishing three sorts of excommunication: minor excommunication, formerly incurred by a person holding communication with anyone under the ban of excommunication; major excommunication, pronounced by the Pope in reading a sentence; and anathema, or the penalty incurred by crimes of the gravest order, and solemnly promulgated by the Pope.

So this would be if a Pope explicitly issues an anathema.  When a Council does so, it's like a pre-emptive issuance of the same ipso facto for anyone who pertinaciously adheres to the error that's been condemned.

Here's my take on it:

It's basically the strongest possible form of excommunication, and when it appears in a Council or pronounced solemnly by a Pope, it's also backed by infallibility.  As we know, other forms of excommunication can be unjust (and therefore at not enforced by God), resulting in being banned from the current society of the Church, refusal of the Sacraments, etc.  Anathema, being backed by solemn and infallible authority in a Council, cannot be mistaken and will result in damnation if someone dies under anathema.  In other words, regular excommunication pertains to exclusion from the society of the Church Militant, but doesn't necessarily exclude from the Church Triumphant (if it's unjust, for instance), but someone who dies under anathema would be damned.  Also, other types of excommunication can be lifted or absolved, but a Council decision is final and there's no absolution for someone who remains pertinacious in the error that has been condemned by anathema.  Someone could be excommunicated for having an abortion, but then this can be absolved and lifted.  But an anathema from a Council or solemn teaching of a Pope cannot be lifted until the individual has rejected the error.  Anathema connotes that your poison, rotten, not in a state of grace, and contaminated / polluted, and so also implies vitandus.  Someone who's excommunicated for, say, abortion, is not vitandus.

Bishops can excommunicate, but only the Pope (or Council with Pope) can issue an anathema, since it's infallible and solemn.  Whereas a Bishop might be mistaken or unjustly excommunicate someone, an anathema being a solemn pronouncement of a Pope/Council would be infallible (similar, IMO to the canonization of a saint).  Someone who dies under a papal anathema is certainly damned, whereas someone who dies under excommunication could be saved, having only been excluded from the society of the Church Militant, and possibly unjustly.