!
The exclamation point (punctus exclamativus) was invented in the mid-14th century by scholars of the ars dictandi (art of document creation), a movement centered around Bologna. Around 1360 one Iacopo Alpoleio da Urbisaglia listed it as one of eight signs of his own invention. The author of an earlier Ars punctandi, in which the sign is first proposed, is unknown. (This work is often attributed to Petrarch, apparently erroneously.) The first known appearance of the sign in actual use dates from 1399 in the work of Coluccio Salutati, to whom some modern scholars have attributed its invention.

Some sources assert that the symbol is a condensed version of the interjection io (a Latin equivalent to “huzzah”), but this is almost certainly apocryphal, considering that most of the other punctuation marks invented within the ars dictandi were, like the exclamation point, variations on the simple point or period.

@
Neither the historical nor the graphical origin of the at sign (or “commercial at”) is known. Competing theories have it that the symbol is, among other things, a condensation of the Latin ad, or a shorthand version of the French à. All such theories are apparently pure speculation. Around 2000 a scholar claimed in the press that he had discovered the “earliest known” appearance of the symbol in a 1536 Italian commercial letter (with a tallying function similar to its modern use), and this claim is still widespread online. But the symbol has since been shown to have been used in a similar commercial function in Spain at least a century earlier. And it appears in Byzantine manuscripts well before that, but purely as a scribal adornment of the Greek alpha, with no special signification. In 2012 scholars brought such an appearance of the symbol, in a Byzantine-influenced Bulgarian manuscript of c. 1345, to the attention of the press. These same scholars nonetheless still asserted that the Byzantine scribes had in turn surely borrowed the form from the Latin, where it was derived from ad.

#
It has been claimed by at least one scholar (and thereafter reported by many others) that the number sign (or “pound sign”) originates with the abbrevation “lb.” for “pound” (derived from the first word in the term libra pondo, meaning essentially “a weighed pound”). This abbreviation, often written by hand in an uninterrupted movement and thus linked by a horizontal stroke, was afforded a special symbol by printers, ℔, with a bar connecting the two letters. Supposedly this symbol was eventually subjected to further abstraction to produce the modern “pound sign.” This history, however, does not seem to be at all well documented (at least not online!), nor is the purported chronology clear.

In my minimal internet searching, the earliest documented appearances of the symbol in its modern form seem to be from the late 19th century, and it seems to come into regular typographical use only in the early 20th century.

$
There are many apocryphal claims about the origin of the dollar sign, but there does seem to be a respectable consensus that its actual origin is as a condensation of a P with superscript S, P^S, an abbreviation for peso in colonial America, where the Spanish dollar was the standard currency. When written by hand in an uninterrupted movement, the upward stroke toward the S creates the vertical bar; in the variant with 2 bars, the second bar is a vestigial form of the P. These two forms are contemporaneous alternatives, of equal authenticity: the earliest documented appearances of both versions are apparently in documents from the 1770s. The symbol was first rendered into type some time after 1800.

%
The percent sign originated in the abbreviation of per cento as p c^o, traced back to 15th century Italian manuscripts. Gradually the superscript o began to be written directly over the c. By the 17th century, the p had been stylized into a horizontal bar and otherwise eliminated; the symbol had a horizontal form, similar to the division symbol ÷ but with circles rather than points. The oblique form is “of modern origin”; exactly how modern is not clear.

^
The circumflex originates in Ancient Greek orthography, where the acute and grave accents marked vowels with rising and falling pitch respectively; the circumflex symbol, which combined the two visually, was used for single syllables containing vowels of rising and falling tone successively.

The caret, indicating editorial insertion (Latin caret: “it lacks”) is a distinct symbol, presumably with its own history, about which I can unfortunately find almost no information, apart from the claim that its current editorial use is identical with its historical use. I do not know whether the caret sign bears any genetic relationship to the circumflex or whether it is simply a form of arrow, which is a symbol of prehistoric origin.

&
The ampersand symbol derives from a ligature for the Latin et, “and.” Early forms of the handwritten ligature are of Roman origin and date back to the first century AD. The ligature very gradually became more stylized and medieval scribal forms resembling modern ampersands had developed by the 6th century.

*
The representation of a star as a radially pointed shape is apparently of prehistoric origin, and the use of such a symbol as a logogram goes back at least to ancient Sumerian writing. I have had difficulty finding any more specific information about the evolution of the “modern asterisk,” perhaps because there is in fact nothing in particular to distinguish this star symbol from any other.

( and )
Brackets were invented by the same 14th-century humanists cited above in connection with the exclamation point. Exactly as with the exclamation point, the first known appearance of brackets in print comes from a 1399 work by Coluccio Salutati, in which the brackets are asymmetrical and angled. A 1428 manuscript has examples of symmetrically paired angled brackets. The rounded form was recommended by Gasparino Barzizza, and appears in print by 1470.

Readers, please correct all errors and supply all missing information in the comments. Thanks.