Optical clocks have moved to the forefront of frequency metrology. Their outstandingperformances enable the exploration of new fields of research such as the search for darkmatter and dark energy [1, 2], temporal drifts of the fine structure constant alpha [3, 5], violationsof the Einstein equivalence principle (EEP) [6], and new applications such aschronometric leveling [7]. State-of-the-art optical clocks outperform the current realizationof the SI-unit "Second" by the 133cesium fountain clocks, by two orders magnitudeor more in instability and accuracy which triggers a discussion on a re-definition of thesecond. In 2016 the Consultative Committee for Time and Frequency (CCTF) of theInternational Bureau of Weights and Measures (BIPM) released a roadmap towards a redefinition of the SI second. One of the requests is the characterization of the systematicuncertainty of at least three independent clocks at the level of 10^-18. In this work, PTB'snew cryogenic strontium lattice clock, Sr3, operating on the 1S0 - 3P0 clock transitionin neutral 87Sr is described. Its systematic uncertainty has is evaluated to 2.7 x 10^-18 infractional frequency units. This represents an improvement of more than a factor of 5compared to its predecessor system Sr1 [8]. In Sr1 the dominant contribution of frequencyuncertainty was about 1.4 x 10^-17 from the uncertainty of the black-body radiation (BBR)frequency shift. It arose from temperature gradients across the in-vacuum magnetic fieldcoils that are placed close to the atoms. Reducing the gradients was not possible which ultimatelylimited the systems achievable systematic uncertainty. Sr3 features an in-vacuumdual-layer environment, the cryostat, that provides a very homogeneous temperature distributionfor the atoms. This translates to a lower BBR frequency shift uncertainty asSr1 at room temperature operation. The corresponding total systematic uncertainty forroom temperature operation was evaluated to about 3.5 x 10^-18. Furthermore Sr3 featuresa closed-cycle pulse tube cooler that allows to operate the cryostat at any temperatureranging from room temperature to about 80K to further reduce the BBR frequency shiftand uncertainty where the systematic uncertainty reaches the value of 2.7 x 10^-18 as mentionedabove.Sr3 also features an arrangement of electrodes that allow the characterization of thedc-Stark frequency shift in three dimensional space. In this work the characterization ofthe electrode arrangement is described and the determination of the dc Stark shift. In Sr1the this capability was limited to one direction that was pointing along the quantizationmagnetic field axis.During clock operation of Sr1, several high-accuracy comparisons to other atomicclocks have been performed. This includes many absolute frequency measurements yieldingin a new record uncertainty in the transition frequency. An absolute frequency of Sr1of f(Sr1) = 429 228 004 229 873.00(7)Hz [8] was measured that is in agreement withe the onemeasured of Sr3 of f(Sr3) = 429 228 004 229 872:94(19)Hz. The statistical uncertainty the measurements was significantly improved by using a H-Maser as a flywheel oscillator toeither extend the dataset or to bridge downtimes of the Sr-clocks [9].Optical frequency ratio measurements between either of the two strontium clocks andthe on-campus 171Yb+ single-ion clock have been carried out [10] for direct determinationof their frequency ratio beyond the limitation of the primary frequency standards representedby Cs fountain clocks. The ratio measurements involving Sr1 span over a period ofmore than seven years and more than half a year with Sr3. The measurements have alsorevealed that the frequency ratio of the clocks, are reproducible within their uncertaintieson short time scales but exhibits unexpected large scatter in the long term. The observedvariations are on the order of several 10^-17 which is beyond any of the clocks reportedsystematic uncertainty. Despite an excessive search no uncontrolled frequency shifts werefound.In the near future the in-vacuum cryostat is supposed to be updated with rotatableshutters. They will allow to minimize the BBR shift uncertainty during cryogenic operation.Prospectively a BBR shift uncertainty at the low 10^-19 level can be expected whichpaves the way for the system to reach a total systematic uncertainty of below 1 x 10^-18.