  Leading logarithmic corrections to the difference of Lamb shifts of s-states
$E_L(1s)-8E_L(2s)$ and to the life time of $2p_{1/2}$ state are considered. The
result of Sokolov and Yakovlev for the Lamb splitting of $2s_{1/2}$ and
$2p_{1/2}$ is re-evaluated and our new value is 1057.8576(21) MHz. Using value
of $E_L(1s)-8E_L(2s)=$ -187.237(8) MHz, obtained here, a new value of the
Hydrogen and Deuterium ground states using all recent measurements connected
with 1s or 2s Lamb shifts. The highest precision value for the Hydrogen ground
state is obtained from corrected result of Sokolov and Yakovlev experiment as
8172.934(22) MHz.
  The Deuterium result is $E_L(1s)-8E_L(2s)=$ -187.229(8) MHz, using it we
obtain from the Garching experiment 8183.905(224) MHz.
  Some related topics are also considered. Taking into account nearest future
result the fine structure constant problem are reviewed. Special attention is
payed to Muonium hyperfine splitting, which it is done simillar to Lamb shift
calculatuion for and to the neutron de Broglie's wave length measurements which
also could lead to some connection between the Deuterium mass and the fine
structure constant.
