Logseq allows you to freely publish notes using custom domain or GitHub pages. Using the below steps, you can accomplish that.

Terminology

Before going ahead, let’s clear up some terminology.

PKM: Personal knowledge management, collecting information.
Backlink: Link to the referred resource/note. Mostly you will refer to another note by surrounding them with double square brackets ([[test]] to link test note)
Bidirectional linking: if Note A refers to Note B, then Note B has Backlink to Note A. (A <=> B)
Graph: Shows all the connections between notes. Some apps like Roam Research & Logseq refer to graph as a database (collection of your notes), whereas Obsidian refers to vault as a database.

Publishing notes - Roam vs. Obsidian vs. Logseq

Roam Research, Obsidian and Logseq provide bidirectional linking between notes and graph views of them.

To use Roam Research, you need to pay monthly/yearly (15$/month at this time of writing), and it allows you to create up to 3 graphs that you can store in their cloud. You can make a graph public to publish your notes. There are other services like Roam Garden which provide a more excellent UI to your notes; this is paid service (7.5$/month).

Obsidian allows you to use any folder to store your notes. All your notes are stored locally, and you can sync with any service like Syncthing, Resilio Sync, Google Drive, Dropbox, Github. Obsidian also released an Obsidian Sync feature (8$/month), where all the notes are encrypted locally with your password and sent to their servers (more secure than Roam Research). They provide an Obsidian Publish service for publishing notes, which costs 16$/month.

With Logseq, you can choose any local folder (can be synced to the cloud) to store notes; for publishing notes, they provide an option to export Graph to HTML pages, and you can deploy this to your server or domain or GitHub pages or IPFS.

Steps to publishing notes using Logseq

Note that you can import notes from Roam Research as JSON and import them to Logseq.

Set homepage

After selecting the folder to store your graph/database, select ... and choose Settings in the right upper corner. Select the Editor tab and disable “Journals”, once done the “Set the default home page” option will be enabled; set this to any name you would like to name your home page. Create a new note/page with the same name.

You can also make this change directly in config.edn file, go to Settings => General tab => select Edit config.edn,

will open config.edn, search for default-home and set default home page like below

:default-home {:page "Home"}

Note: You can get config.edn by using search, keyboard shortcut is Cmd+k or Ctrl+k depending on macOS or windows.

Set pages public

You have two options,

Publish all notes. For this, go to Settings, select Editor, and enable All pages public when publishing.
Select what notes you want to publish by selecting Make it public for publishing

Set custom theme

To change the default theme, go to Settings => General tab => “Edit custom.css”, here you can add your custom CSS. There are many themes available; refer to this, pick any theme you like, copy the theme custom.css content, and paste in your logseq custom.css.

Export graph/notes

After having your notes, it’s time to export. Settings => select “Export Graph”, select “Export public pages”, select any folder where you want to store the generated static files from your notes. You can open the index.html in this folder to preview.

Deploying notes

You can deploy the folder containing the generated static files from above to Github pages, Vercel or Netlify. You can also deploy this folder to decentralized network using IPFS, refer this post. Here is a sample graph I deployed, https://logseq.rajashekar.org.

Previewing linked notes

Hovering over links, shows preview of the note.

Math equations

Below is how math equations will be shown.

Drawings

Excalidraw drawings are not displayed, but you can copy the diagrams as png and include them.

Org Mode

Logseq supports Org Mode and has some nice font icons - you can refer to this cheatsheet

Viewing graph

Clicking on the Graph view will show links between notes. Here is preview of the graph I deployed.

Backlinks

Below is how backlinks are shown.

Searching notes

Pressing Ctrl+k (for Windows) Cmd+k (for macOS) will pop up the search bar, and you can search all your notes.

Presenting slides

Last but not least, you can present a page/note as a slide. Click on “Presentation” in page settings, and press f to present in full screen. Below is the demo.