Very Low-Level Linux

I'm starting a project using the Linux kernel as a text-based system. I was wondering on how to go about getting just a very basic kernel running. I want to end up with the following in the stripped down OS:

Basic keyboard drivers

Basic text-based interface with prompt

Default network drivers with basic configuration options

Just enough drivers to run a very low-level graphics card with ability to detect HDMI resolution (no actual graphics will be required)

If there is already a distribution out there with these features and NO GUI, I would like to hear about it and the features it includes. Thanks to all who respond.

Have you done Linux from scratch?

http://www.linuxfromscratch.org/

It walks you through building the linux kernel and necessary packages for a minimum system, and if you modify the kernel, you could end up with just what you're talking about.

0.0 Wow. This looks like the kind of thing I was looking for. A bit of a big task by the looks of it, but I think it might be what I need. It would be helpful if you had an OS to suggest while I'm writing the actual software to test with if you know of any stripped down distros meant for low-power machines.

I'll definitely end up building a Linux distro from scratch with this (very) in-depth book, though. Now I just need to find a place to print this...

Any number of distros allow you to build a basic system - minus GUI.
None will have (such) a minimal kernel as they have to ship a kernel (plus initrd) that still boots on any one of the almost infinite combinations of hardware out there. Easy enough to rebuild the kernel later.
Personally I have liked Arch for the last little while - you add what you want the system to have, rather than having to take stuff out.

lfs is a different philosophy altogether; that's the whole kit and kaboodle - toolchain and all.

"very low-level graphics card with ability to detect HDMI resolution (no actual graphics will be required)"

Kind of conflicting there.

Almost all hardware in linux needs some sort of driver.
Almost all video cards can run in vesa mode but not sure you could run hdmi. Never tried it. May work.

Well, I'm running Linux on the machine I'm using now. When it starts up, before it has any video drivers to speak of, it adjusts the resolution at boot to match the TV it's connected to (1080p). I'm just wondering what kind of coding is required to poll that information. Obviously, they've updated HD displays to send that information back to the OS if it is polled. At least, I've never seen a VGA port do that accurately. In any case, I will be using the same video card throughout all of my machines and therefore won't need to worry about what video drivers they are. It will just be included with the OS. I'm just wondering what distro will have the essential keyboard drivers (essentially all of them) and the ability to put text out to the screen at the correct resolution without having to manually set it. And of course, if the display, for some reason, doesn't report back its resolution, it will default to a 640x480 and the user can manually set it later.