I have been working for a company for almost 1 year. Last month, there was an internal workshop which I was interested to attend.I asked my manager. I send her my Expression of Interest. After a couple of days she told me that I can attend the next workshop. Four of my colleagues(everybody except me and one of our senior staff) attended the course. (one of them made redundant after 2 weeks). Now I want to attend some workshops to improve my skills and probably looking for another job.(I want to pay by myself because I know that she will say she can not pay for the trainings). Do you think if it is better to let her know that I am attending these workshops or Not? Any advice?
Let her know. It can't hurt you, and she may even end up paying for the trainings (though if they're internal I can't see why there'd be a fee to begin with). Good companies with good management want their employees to improve themselves and learn in any way possible--whether that's through reading, mentorship, or attending workshops. Telling your boss you're excited to attend trainings will only show her your strive for better performance.
It really depends on the outcome you want.
No manager will fault you for paying for training that you attend on our own time. The real question you have to ask yourself, is why do you think you should tell her?
If you are hoping that maybe there is a chance that they will cover the funding, or at least part of it, then you have to tell your manager with enough notice for them to gather the funds required.
If you are not seeking funding, then maybe you are fishing for a promotion (which there is nothing wrong with). In this case, you are letting your manager know how serious you are about this job and that you will probably be qualified for a promotion if you continue to improve yourself.
In the event that none of the above is true, I can't imagine why you would want to tell them. There is absolutely no harm in telling your manager about this, in fact it more likely that they will not even care to hear it, unless there is a reason like I stated above. This would roughly be the same thing as discussing a concert you saw over the weekend. If you don't have a reason to tell her, I personally would not.
I try to keep my workplace relations very professional, so if there no reason to tell my manager about something I did on my own time, I just don't do it.