I NEED A LIST OF HARDWARE COMPONENTS ASSEMBLY OF THESE HARDWARECOMPONENTS AND SOFTWARE PROGRAMMING
Please do not yell at us.
Tell us in a normal calm way what you are planning to accomplish.
Are you asking for someone to do this for you? This is mostly a do-it-yourself forum and the Arduino is a do-it-yourself platform, so if you want some help getting started we can help.
Otherwise, look for a multimeter with a computer connection. It will cost you a few hundred dollars (or more) but it's cheaper than paying someone to build you something custom.
The Arduino has ~1mV resolution if you use the optional 1.1V reference. Below that, you'll need an amplifier.
I assume you also need a display, and depending on how much data you need to store you may need some additional memory.
The software should be trivial. [u]Read Analog Voltage Example[/u] should get you started.
When is your assignment due? As for a logger, as pointed out, you can get a multimeter that hooks to your computer and do it that way. You can get one like THIS for about $70. There are quite a few others in the same price range. You need to define your requirements as to what the resolution is, how fast it needs to be and what type of hardware you need.