You can thank Petrarch for all the sonnets you have to read in school. This 14th century Italian poet isn’t the first person to write sonnets, but he makes the form popular all across Europe, including England. He is the Elvis Presley of the sonnet. But, just as with rock 'n' roll, new poets keep fiddling with the sonnet form, tweaking it slightly to fit their needs. Shakespeare, for example, uses a different form of the sonnet, which we call "Shakespearean" for that reason. But, Donne stuck to the original. Mostly.
The Petrarchan sonnet has fourteen lines and a rhyme scheme that goes ABBAABBA and then, most frequently, CDCDCD. But, "Death, be not proud" finishes slightly differently. Its last six lines are CDDCAA. If you look closer, there’s even more weird stuff going on at the end. For example, line 13 has a word near the end, "swell’st," that rhymes with "dwell" and "well" from the previous two lines. He just sticks a rhyme in the middle of the verse: very strange. And, the last two lines don’t seem to rhyme well at all: "eternally" and "die." You have to pronounce it "eternal-lie" to make the rhyme work. No one is sure exactly what Renaissance English sounds like, so it’s possible that they did pronounce the word this way. But, it’s also possible that Donne wanted the rhyme scheme to fizzle out at the same moment when death "dies."
Another feature of a Petrarchan sonnet is a shift, or "turn," in the argument or subject matter somewhere in the poem. In Italian, the word is volta. Usually, the turn occurs at line 9 to coincide with the introduction of a new rhyme scheme. That’s the case for "Death, be not proud," although the turn isn’t major. The speaker sharpens his attack and starts calling Death names, but he doesn’t fundamentally change his argument. If you want to rebel, you can argue that the real turn doesn’t happen until the middle of the last line, when Donne drops this shocker: "Death, thou shalt die." At the very least, we think it’s the most surprising move in the poem.
Finally, the Petrarchan sonnet has a regular meter: iambic pentameter, which means that each line has ten syllables, and every second syllable is accented. That’s the reason, for example, that "Thou art" has to be condensed into one mouth-cramming syllable, "Thou’art" in line 9. Otherwise, there would be eleven syllables in the line.
But, what about the first line? For one thing, it begins on an accented beat: DEATH. Truth be told, Donne’s pretty loose with his iambic pentameter. For him, iambic pentameter is less of a rule and more of a general guideline, like that "No Horseplay" sign at your local pool. Of course there’s going to be horseplay! It’s a pool! And Donne sometimes counts a big pause as a syllable, which is why line 1 seems to only have nine syllables: because of the pauses in the line, it takes at least as long to recite.