The four main types of academic writing are descriptive, analytical, persuasive and critical. Each of these types of writing has specific language features and purposes. In many academic texts you will need to use more than one type. 

Descriptive: The simplest type of academic writing is descriptive. Its purpose is to provide facts or information. An example would be a summary of an article or a report of the results of an experiment.  The kinds of instructions for a purely descriptive assignment include: 'identify', 'report', 'record', 'summarise' and 'define'.

Analytical: This writing includes descriptive writing, but also requires you to re-organize the facts and information you describe into categories, groups, parts, types or relationships. 

Persuasive: In most academic writing, you are required to go at least one step further than analytical writing, to persuasive writing. Persuasive writing has all the features of analytical writing (that is, information plus re-organizing the information), with the addition of your own point of view. Most essays are persuasive, and there is a persuasive element in at least the discussion and conclusion of a research article. 

Critical: It has all the features of persuasive writing, with the added feature of at least one other point of view. While persuasive writing requires you to have your own point of view on an issue or topic, critical writing requires you to consider at least two points of view, including your own. 

The University of Sydney (2022)