The sonnet is one of the poem styles which place a poet within a creative box. Confining the poet within a strict set of rules for his composition, creativity is actually released within those limits.
By definition, a sonnet is a 14 line poem, in iambic pentameter with specific rhyme schemes. Iambic pentameter is a meter which contains 5 iambic "feet", which will be 10 syllables with the stress on the even syllables. This meter most closely resembles the pattern of English speech. Blank Verse is unrhymed iambic pentameter. The plays of Shakespeare are written in Blank Verse.
Sonnets originated in Italy the 13th century. Italian sonnets, generally known as Petrarchan sonetts, follow the basic pattern of eight lines and six lines. The initial eight lines being called an Octave or Octet, containing what's known as the Proposition. The six lines referred to as the Sestet, contain the Resolution. The first line of the Sestet is called the Volta, or the turn.
The standard Petrarchan sonnet has a rhyme scheme ABBAABBA CDECDE
The Crybin variant is where the Octave's rhyme scheme is ABBACDDC
A Sicilian Sestet has a rhyme scheme of CDCCDC
An English sonnet, also referred to as Elizabethan or Shakespearean, is made up of three quatrains with a final couplet. Instead of the proposition in an Octet and resolution in a Sestet, an Elizabethan sonnet will generally present the theme of the work three different ways or viewed from three different angles with a couplet at the end wrapping up the concept. The English sonnet generally will have a rhyme scheme of ABAB CDCD EFEF GG
A Spenserian Sonnet is an English sonnet with a rhyme scheme of ABAB BCBC CDCD EE This form links the quatrains together via the rhyme scheme.
Terza Rima is a sonnet using four tercets (three lines) with a final couplet. It utilizes an interlocking rhyme scheme (like a Spenserian sonnet) which will generally be ABA BCB CDC DED EE. (Although my first Terza Rima, Ignore the Dark, used AA for the final couplet as I specifically wanted to link the couplet with the ryhme in the first tercet.)
Never having attempted a Miltonic Sonnet, I won't here comment.
These are the basic forms of "Sonnetry". Exceptions are common, both with rhyme scheme, percentage of rhyme and the meter. Experimentation is acceptable up to the point where it can't really be called a sonnet anymore. As in all art, beauty is in the eye of the beholder.
Frank Garnick