[sentence (plain form)] + との + [noun]
との is a combination of the quotative particle と and the possessive/modifying particle の. It is used to turn a quoted statement, thought, or piece of information into a noun modifier, allowing you to attach that content directly to a noun. In other words, との lets you say "the [noun] that [statement]."
This pattern is extremely common in written Japanese – news articles, reports, formal correspondence – and also appears in spoken Japanese when relaying information, opinions, or decisions.
When you want to modify a noun with a quoted clause, you use との before the noun. Compare:
In the second sentence, こない来ないと (the quotative content) modifies れんらく連絡 (message) via の.
との frequently appears before nouns that represent information or communication, such as:
Both との and という can modify nouns with quoted content, but they differ in nuance:
Compare: さんか参加できないというへんじ返事をもらった is also natural but slightly less formal.
The expression とのことだ (or polite とのことです) is an extremely common set phrase meaning "I'm told that…" or "it is said that…" It is used to relay secondhand information in a formal or polite manner.