Telkit is designed for Minecraft 1.7.10.
It is available on the Technic Launcher. The current release of Telkit is version 5.0.4, released on Wednesday, September 6, 2017.

Custom Sphax Patches (In Menu Loading Order, Top to Bottom)
Sphax PureBDcraft Modded Textures for Telkit - June 30, 2017 for Telkit 5.0.3+
These patches are notorious for not working if Telkit is allocated less than 10 GB of RAM.

Basic Prerequisites (Exceeding These Is Fine)
Technic Launcher
Java Development Kit 8 x64

If you wish to play around with the file, here is the direct download link.

Vanilla Minecraft Packs Compatible with Telkit
VoxelBox Scientific HD (1.6.1+) - superseded by NosLabs Custom Blocks mod
Original NosLabs Resource Pack (1.6.1+) - superseded by NosLabs Custom Blocks mod

Nosiphus Modded Server

The Nosiphus modded server is the single most important thing we ever brought into existence. Once a plain vanilla 1.5.2 server, it has grown to be powered by Telkit, a 135-mod behemoth.

Once almost impossible to access, the Telkit modpack now includes the IP built-in.
Installation Video

Installation Instructions - Courtesy of Nate Sawyers