Commuting to and from work is not deductible. You cannot claim mileage for your commute to work.
You can never deduct commuting to your usual work place, either for employees or self-employed.
Under the tax reform law of 2017, W-2 employees can't deduct work-related expenses even if they are not commuting.
Self-employed workers may be able to deduct travel expenses when they travel away from their usual work location for a temporary assignment. Those rules are shown in chapter 4 of publication 463.
No. Commuting expenses are not deductible, neither are miles driven as an employee regardless of how far you drive or if you drive to different places using your own vehicle during the day. Employee job expenses are not federally deductible.
If you are self-employed and driving to various jobs, then this would be considered business miles and would be a deductible expense.