Hello NEW User here 
I cannot install the packages like #library, #tidyverse or so.
I followed the instructions on the website to download CRAN(extra) and Rtools43, but it always suggests "library cannot be written" after running the codes "install.packages("library"). So basically I cannot start on my work at all!!!
Can anyone help??? Thank you in advance for your help!!!
Rtools43 is used for R-devel, the development version of R and is intended for R 4.3.0. What R version are you running?
Can you please post the complete console output you get? Package installation problems are very specific so we need as much details as possible.
I'm using R 4.2.2, but I also tried Rtools42. Same in consoles.
It seems to be something wrong with the Save Path. According to the Console I have to download the Packages in a specific location. But I would like to use my personal library and create different folders and put in different location.
The newest progress is that I have deleted the software. 
Please post the complete console output you get "as is" , it is hard to guess based on what you are paraphrasing
install.packages("library")
WARNING: Rtools is required to build R packages but is not currently installed. Please download and install the appropriate version of Rtools before proceeding:
https://cran.rstudio.com/bin/windows/Rtools/
Installing package into ‘C:/Users/SMO/AppData/Local/R/win-library/4.2’
(as ‘lib’ is unspecified)
Warning in install.packages :
package ‘library’ is not available for this version of R
A version of this package for your version of R might be available elsewhere,
see the ideas at
install.packages("tidyverse")
WARNING: Rtools is required to build R packages but is not currently installed. Please download and install the appropriate version of Rtools before proceeding:
https://cran.rstudio.com/bin/windows/Rtools/
Installing package into ‘C:/Users/SMO/AppData/Local/R/win-library/4.2’
(as ‘lib’ is unspecified)
trying URL 'https://cran.rstudio.com/bin/windows/contrib/4.2/tidyverse_1.3.2.zip'
Content type 'application/zip' length 428953 bytes (418 KB)
downloaded 418 KB
Have I successfully installed the packages or not?
Also, I am confused about the Save Path. For example:
Installing package into ‘C:/Users/SMO/AppData/Local/R/win-library/4.2’
(as ‘lib’ is unspecified)
This Save Path is just too long, so I want to keep it short so that easier for me to find the files or so. Not sure if I correctly described the issues. Anyway, it seems that if I change the default path to save, then I could not run the packages or so...
Are you sure that there is a package called "library"? I have never seen one and did not find anything with that name on CRAN. Given that libraries are where installed packages are stored on your computer, it would be a strange name for a package.
This is my complete console output when successfully installing the broom package:
install.packages("broom")
Installing package into ‘/Users/john/Library/R/x86_64/4.2/library’
(as ‘lib’ is unspecified)
trying URL 'https://cran.rstudio.com/bin/macosx/contrib/4.2/broom_1.0.2.tgz'
Content type 'application/x-gzip' length 1855296 bytes (1.8 MB)
==================================================
downloaded 1.8 MB
The downloaded binary packages are in
/var/folders/wd/szl0t39j28vbgh7z0039gbh40000gp/T//RtmpcGyZjl/downloaded_packages
Oh I think you are right. library() is then a function that I use to run "tidyverse".
In my case do you think I should download Rtools? Where should I put the Working Directory folder?
At the moment I have 2 folders, one is R (including Library, I suppose in the library are the installed packages richt?), the other one is RStudio. And then there is a CreatorTem folder. In general, I am confused about the Data Management. I don't know where I should put a folder, and which folder is for what.
I think the problem has been solved. Thank you for your help on this issue! 
This is the default user-level package library, it is possible to define a custom location for this if you want but under normal circumstances you would never need to manually access this files so I would recommend you to just leave it as is for the time being.
In case you really want to modify the location of your package library, here you can find how to do it:
Packages only need to be installed once with the install.packages() function but they need to be loaded with the library() function on each R session you want to use them.
RTools is used for compiling packages from source, you would only need it if the package you want to install is not currently available as a precompiled binary. For the latest R version (currently the one you are using) precompiled binaries become available a couple of days after a new package version is released so unless you are in a hurry to install an specific package version that is not currently available as a binary, you don't necessarily have to install RTools, although, there is no harm if you do.
The working directory is a dynamic concept, you usually set it per project to a folder containing the files for that specific project and you change it when you want to work on another project.
Although, if you are using the RStudio IDE, a better workflow is to create an "RStudio Project" and that will automatically take care of the working directory for you. You can learn about this workflow here:
I believe you are overthinking this, you should have a "root" folder containing all necessary files for each project you want to work on and that's it, under normal circumstances you shouldn't have to worry about any other folder, leave this issue for when it is actually needed, like when you get an error message saying it has problems with some folder location.
This is amazing! THANK U for the thoughtful explanation! 
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