In this paper, the first of a series of papers on optimal battery charging, we present a closed-form solution to the problem of optimally charging a Li-ion battery. A combination of three cost functions is considered as the objective function: time-to-charge (TTC), energy losses (EL), and a temperature rise index (TRI). First, we consider the cost function of the optimization problem as a weighted sum of TTC and EL. We show that the optimal charging strategy in this case is the well-known Constant Current-Constant Voltage (CC-CV) policy with the value of the current in the CC stage being a function of the ratio of weighting on TTC and EL and of the resistance of the battery. Then, we extend the cost function to a weighted sum of TTC, EL and TRI and derive an analytical solution for the problem. It is shown that the analytical solution can be approximated by a CC-CV with the value of current in the CC stage being a function of ratio of weighting on TTC and EL, resistance of the battery and the effective thermal resistance. Index Terms battery charging, optimal charging, time to charge, open circuit voltage, state of charge.