Create a category of “Brands”

Goto Catalog --> Manage Categories and create a new category with Display mode: "static block only"

Magento Navigation

Add the following code to the "description" field

Create a static block

Goto CMS --> Static Blocks --> Add New Block and create a new static block with the ID like "wp_custom_menu_310", where "310" is the category ID of the brand category. Add the following code to the "Content" field:

Magento Navigation

Change images

Images can be found here: /YourMagentoDir/media/template/brand/

Change links

Simple way

Specify the brand name to search for, and copy the link on the search result in the browser. It will be something like "/catalogsearch/result/?q=Addidas"

Right way

You can use Better Store Search:betterstoresearch.com

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