A man accused of planning terrorist attacks against left-wing organisations in Melbourne went online to learn how to make explosive devices and to research his intended targets, his trial has heard.

Prosecutors allege Phillip Michael Galea was in 2015 and 2016 writing a document titled "The Patriot's Cookbook", which drew on the published works The Anarchist's Cookbook and The Terrorist's Handbook, and which he hoped would prompt "fellow patriots" to initiate "thousands upon thousands of terrorist acts" on left-wing and Muslim targets.

Phillip Galea is led into court on Monday. Credit:AAP

Trades Hall in Carlton was among the targets, a Supreme Court jury heard on Monday, along with Melbourne's Resistance Centre in Swanston Street and the Melbourne Anarchists Club in Northcote.

Mr Galea also allegedly read about the use of piano wire in a garrotte and the manufacture of smoke bombs.