Dictionary.com

noun, plural her·e·sies.

1. opinion or doctrine at variance with the orthodox or accepted doctrine, especially of a church or religious system.
2. the maintaining of such an opinion or doctrine. Roman Catholic Church.
3. the willful and persistent rejection of any article of faith by a baptized member of the church.
4. any belief or theory that is strongly at variance with established beliefs, customs, etc.

Etymonline.con

“doctrine or opinion at variance with established standards” (or, as Johnson defines it, “an opinion of private men different from that of the catholick and orthodox church”), c. 1200, from Old French heresie, eresie “heresy,” and by extension “sodomy, immorality” (12c.), from Latin hæresis, “school of thought, philosophical sect.” The Latin word is from Greek hairesis “a taking or choosing for oneself, a choice, a means of taking; a deliberate plan, purpose; philosophical sect, school,” from haireisthai “take, seize,” middle voice of hairein “to choose,” a word of unknown origin, perhaps cognate with Hittite šaru “booty,” Welsh herw “booty;” but Beekes offers “no etymology.”

The Greek word was used by Church writers in reference to various sects, schools, etc. in the New Testament: the Sadducees, the Pharisees, and even the Christians, as sects of Judaism. Hence the meaning “unorthodox religious sect or doctrine” in the Latin word as used by Christian writers in Late Latin. But in English bibles it usually is translated sect. Transferred (non-religious) use in English is from late 14c.

Discussion/Explanation

This term’s use can often get foggy when speaking historically and is often confused with or treated equivalent to apostasy. Whether used to mean “sect” or simply any who are at odds with the official doctrine, the fact remains the same that those considered in heresy are outside the accepted doctrine.

Many Protestants would consider Roman Catholics as heretical though the same could just as easily be said in reverse. There are significant differences between the two despite their similarities such that you cannot truly consider them the same faith without ignoring significant differences.

Various other heresies would include (but not limited to): Deism, Docetism, the various Gnostic heresies, Arianism, prosperity gospel, LDS church (Mormon), and many more. Many of these and more would also be described as apostate at the same time.

See the apostasy link above for further discussion, compare/contrast, and other articles on this topic.

Τhis first chart lays out the 4 sections of the quad chart. Each section is labeled with a referring letter (Α, Β, C, & D). These are commonly used to reference the endings used for the various verb forms (you can see these forms listed next to their respective letter below). As an example, the Present Active verbs would use the endings found in the A quarter of all the charts below.

The following chart gives the verbal endings with the combining vowel included.

The following chart gives the verbal endings without the combining vowel included.

This chart provides an example of the verbal endings in use.

Note: there are plenty of charts out there that combine all of the above into 1 single chart but this creates a clutter for someone such as myself that can be distracting – particularly if I’m trying to study just one part of the chart. This is why you see the information split up the way you do.

Another key chart to learn and memorize when studying New Testament Greek is the square of stops. This becomes important as you deal with word endings that change.

Use the following for memorization practice. 

Just scroll back and forth between these two tables to challenge yourself. I do this by making the part I don’t want to look at, at that moment, be not visible to my eyes by simply scrolling that table off the screen.

If you’re unfamiliar with the square of stops, it is a tool to help you keep track of the Greek characters that transform when in the presence of certain characters that follow. The + sigma (σ) and the + theta (θ) columns indicate what happens when they are added to any of the characters to the left.